An official said that Mr Liu's remains were cremated "in accordance with local customs and the wishes of the family".
Mozart's Requiem was played at the ceremony, he said.
Photographs shared by local authorities showed Mrs Liu and other mourners beside Mr Liu's open coffin, which was surrounded by white chrysanthemums, a symbol of grief in China.
Later pictures showed Mrs Liu and others on a ship apparently throwing flowers into the sea, during a ceremony to scatter her husband's ashes.
Supporters of Mr Liu say the authorities wanted to avoid providing a burial ground where he could be remembered.
"It was a deliberate move by the Chinese government to hastily arrange the funeral so that no-one can visit his body, which would evoke the most memories," said activist Hu Jia, quoted by the South China Morning Post.
The official who spoke about the funeral said he believed Mrs Liu had been freed, but Mr Liu's lawyer, Jared Genser, rejected this claim and said Mrs Liu had been held "incommunicado" since her husband's death.
"The world needs to mobilise to rescue her - and fast," he wrote in a statement. On Friday, the committee that awards the Nobel Peace Prize said it was "deeply worried" about her and urged China to free her.
At a government-organised news conference, Mr Liu's older brother Liu Xiaoguang said the funeral arrangements had been carried out in accordance with the family's wishes.
Liu Xiaoguang is regarded by Mr Liu's friends as someone who had long disagreed with his brother's views.
Meanwhile in Hong Kong several thousand people held an evening vigil for the dissident, calling him a "people's hero" and demanding "true freedom" for Liu Xia, Reuters reported.
Liu Xiaobo was awarded the Nobel Peace Prize in 2010 for his non-violent struggle for human rights in China.
Kicking off a series of events that will extend into dawn on Sunday, Prime Minister Binali Yildirim told a special session of parliament that 15 July 2016 was a "second War of Independence", following the conflict that led to the creation of the modern state in the 1920s.
"It has been exactly one year since Turkey's darkest and longest night was transformed into a bright day, since an enemy occupation turned into the people's legend," Mr Yildirim said.
Huge rallies are to take place on Saturday, with 15 July declared an annual holiday.
Mr Erdogan will attend a rally in Istanbul on the bridge across the Bosphorus where crowds confronted soldiers. It has been renamed the Bridge of the Martyrs of July 15 and the president will unveil a "martyrs' memorial" there.
Istanbul is awash with giant anniversary billboards and posters showing people confronting pro-coup soldiers, with anti-coup slogans strung between the minarets of mosques.
Mr Erdogan will later return to Ankara to address parliament at midnight (21:00 GMT), the exact time last year it was attacked by coup plotters.
He will unveil a monument to the coup's victims at his palace in the capital at dawn.
On 15 July last year, the coup plotters, armed with tanks, warplanes and helicopters, declared that they had taken over on state media, and bombed parliament and other key locations.
They tried to detain Mr Erdogan as he holidayed in an Aegean resort, but he had left and the coup was thwarted by civilians and soldiers loyal to the president.
The Turkish authorities accused a movement loyal to the Muslim cleric, Fethullah Gulen, of organising the plot.
Mr Gulen, who remains in the United States, denies any involvement.
Washington has so far resisted calls from the Turkish authorities to extradite the cleric.
Mr Erdogan and his supporters may see the defeat of the coup as Turkey's rebirth, but for others it is less triumphant, says the BBC's Mark Lowen, with the memory of the attempt dividing the country.
Critics say Mr Erdogan is using the purges to stifle political dissent, and last week hundreds of thousands of people gathered in Istanbul at the end of a 450km (280-mile) "justice" march against the government.
Its organiser, opposition politician Kemal Kilicdaroglu, condemned the coup but said the measures Mr Erdogan had taken since constituted a "second coup".
The president accused the marchers of supporting terrorism.
On Friday, the government continued its dismissal of state employees, sacking another 7,395 for alleged links to what it calls terrorist groups.
Two men are now charged with the killings of four young men in an affluent Philadelphia suburb.
Cosmo DiNardo and Sean Kratz, both 20, each face murder charges as well as multiple counts of conspiracy, robbery and abuse of a corpse.
Police have confirmed all four men, missing since last week, were found buried on a farm belonging to Mr DiNardo's family.
Both men have confessed to investigators, according to officials.
The accused men - who told investigators they are cousins - allegedly sold the victims cannabis before killing them separately and burning their bodies on Mr DiNardo's family's farm, according to the Bucks County district attorney.
Investigators found the body of Dean Finocchiaro, 19, who disappeared last Friday, in a "common grave" on the 90-acre farm in suburban Philadelphia.
Mark Sturgis, 22, and Tom Meo, 21, also vanished on 7 July, and Jimi Tar Patrick, 19, went missing two days earlier.
On Thursday, a lawyer for Mr DiNardo told US media that his client had confessed to playing a role in the four murders after a plea deal was reached with prosecutors that would spare him the death penalty if convicted.
"I'm sorry," said a shackled Cosmo DiNardo as he left court on Thursday.
District Attorney Matthew Weintraub said on Friday that Mr DiNardo disclosed the location of the one victim's remains as part of the deal.
"Our boys get to go home to their families, which was always our first priority," Mr Weintraub said at a press conference announcing the criminal charges.
The three other bodies had already been discovered by police more than 12.5 ft (3.8m) beneath an old oil tank that had been converted into a "cooker".
Two firearms were also recovered from Solebury Township farm property.
According to a police affidavit, Mr DiNardo told investigators that he had arranged to sell $8,000 worth of cannabis to Mr Patrick, whom he had picked up from his home on 5 July.
After the two walked to a remote part of the property Mr DiNardo shot Mr Patrick with a .22 rifle, investigators say.
On 7 July he allegedly arranged another cannabis sale with Mr Finocchiaro.
He picked up Mr Kratz before driving to the second victim's home to transport him to the farm property, investigators say.
Before then, Mr DiNardo had given a .357 pistol to Mr Kratz.
Mr Kratz shot the man in the head, and Mr DiNardo fired another shot at him as he lay on the ground, police say.
Later that day, Mr DiNardo met Mr Meo and Mr Sturgis and had them follow him back to his family property in their car.
After both men were ambushed and shot, Mr DiNardo allegedly ran over Mr Meo with an earth-moving machine.
He then used the machine to transport the bodies of Mr Meo, Mr Sturgis, and Mr Finocchiaro into a metal tank, which he described to police as a "pig roaster", before pouring gasoline on them and setting the pit on fire.
The two men returned the next day to dig a hole with the earth-moving machine where they placed the men's bodies.
Takeaway delivery firm Deliveroo emailed drivers saying it was working with the Met Police and urged its staff to report any information about the attacks.
The email said the firm was "truly shocked" about what had happened.
The assaults happened amid increasing concern about the sharp rise in acid attacks in London
A Met spokesman said one line of inquiry detectives would be pursuing was whether the attackers were targeting moped riders to steal their bikes.
The 16-year-old boy was arrested in Kingsbury Road, north-west London, early on Friday, while the 15-year-old was arrested in Stoke Newington several hours later.
The attacks began at 22:25 BST on Thursday in Hackney Road.
A 32-year-old man on a moped was left with facial injuries after another moped, with two male riders, pulled up alongside him and threw a corrosive substance in his face.
One of the men stole his moped and the other drove away on the vehicle they arrived on.
The Met said it was awaiting an update on the extent of the victim's injuries. Inquiries are ongoing.
Thursday night attacks timeline
22:25 BST: A 32-year-old man on a moped in Hackney Road is left with facial injuries after a moped, with two male riders, pulls up alongside and attacks him. They also steal his moped.
22:49 BST: A 44-year-old man has a corrosive substance thrown in his face by two men on a moped in Islington.
23:05 BST: A corrosive substance is reported to have been thrown in the face of a 52-year-old man by two men on a moped in Shoreditch High Street. The victim is taken to hospital.
23:18 BST: Police receive reports of a robbery in Cazenove Road, Stoke Newington, where a corrosive substance is thrown. A 24-year-old man suffers facial injuries described as "life changing".
23:37 BST: A 33-year-old man on a moped in traffic in Chatsworth Road, Clapton, has liquid sprayed in his face and his vehicle stolen.
Assaults involving corrosive substances have more than doubled in England since 2012, with the number of acid attacks in the capital showing the most dramatic rise in recent years.
The Met's own figures show there were 261 acid attacks in 2015, rising to 458 last year.
So far this year - excluding Thursday night - the Met has recorded 119 such attacks.
About a third of last year's acid attacks in the capital took place in the London borough of Newham, which is in his constituency.
Mr Timms told BBC Radio 4's Today programme he was "most concerned about sulphuric acid" and that carrying a bottle without justification should be treated as an offence, like carrying a knife.
"We could certainly come up with arrangements that would allow people to use sulphuric acid in the normal way, perhaps with the benefit of a licence.
"But simply walking around the street with a bottle of sulphuric acid, that should be an offence," he said.
A Downing Street spokesman said the prime minister viewed acid attacks as "horrific".
"We are working with the police to see what more we could do. The prime minister's view is that the use of acid in this way is horrific."
Home Office minister Sarah Newton told BBC Radio 5 live Breakfast the government was considering tighter controls on some chemicals in response to the acid attacks in East London and elsewhere.
But she said regulation would be difficult, as "these chemicals are under everyone's kitchen sinks".
She said it was clear acid was being used "as a weapon" and work had been commissioned "to understand the motivation" of people who use it to injure others.
She also said the government was examining sentencing for those who use acid to injure people.
Two German tourists have been killed in stabbings at a hotel beach in the popular Red Sea resort of Hurghada, Egyptian officials say.
At least four other people were injured and a man has been arrested.
The suspect is being questioned by police to determine his motives, the interior ministry said.
The knifeman initially killed the two women before injuring two other tourists at the Zahabia hotel, officials told Reuters news agency.
He then swam to a nearby beach and attacked and wounded two more people at the Sunny Days El Palacio resort before he was overpowered by staff and arrested.
"He had a knife with him and stabbed each of them three times in the chest. They died on the beach," El Palacio hotel Security Manager Saud Abdelaziz said.
Mr Abdelaziz said the injured include two Czechs and two Armenians. All are now being treated in hospital.
The attacker's motive was still under investigation, the interior ministry said.
"He was looking for foreigners and he didn't want any Egyptians," a member of staff at the Zahabia hotel said.
Three foreign tourists were stabbed at the same resort, renowned for its scuba diving, in January 2016 by two suspected militants from the Islamic State militant group (IS).
Initial reports had said those killed were Ukrainian, but Ukrainian officials denied this.
It is unclear whether the attacker had any links to jihadist groups or whether he was psychologically disturbed, officials said.
Egypt's security forces are dealing with an Islamist uprising in the country's Sinai Peninsula. The tourist industry has been targeted by militants in North Africa over the past few years
The United Nations says there was a 50% increase last year in the area of land being used to cultivate coca leaf in Colombia.
The UN estimates that a third more cocaine was being produced in the country in 2016.
The head of the UN Office on Drugs and Crime, Bo Mathiasen, called the increase significant.
Analysts say much of it was due to the end of the eradication of coca crops by spraying.
The report said the total coca-growing area rose from 96,000 hectares in 2015 to 146,000 in 2016.
Mr Mathiasen said that he held out hope for a reduction in cultivation because Colombia had signed a peace agreement with the biggest rebel group in the country, the Farc, which controlled much of the drug-producing areas.
But local analysts argue that the rise was caused partly by a hiatus resulting from the government's peace deal with Farc rebels.
Under the deal, the Farc agreed to relinquish control over drug production areas and help the government try to encourage local farmers to plant substitute crops.
Farmers have taken advantage of the delays while the crop substitution policy is set up to plant coca, which has increased in price by almost 50%, because they know they will be offered subsidies later not to grow the plant.
Meanwhile, the Colombian government has increased by almost 50% its seizures of cocaine - from 253 tonnes confiscated in 2015 to 378 tonnes in 2016.
