Theresa May's offer to give EU citizens in the UK "settled status" after Brexit has been described as being "far short of what citizens are entitled to".
MEPs, including European Parliament chief Brexit negotiator Guy Verhofstadt say the proposal is a "damp squib".
It offers Europeans in the UK fewer rights than Britons in the EU, they say in a joint letter to newspapers.
Cabinet Office minister Damian Green said the "basic rights" of EU citizens living in the UK would be "preserved".
He urged Mr Verhofstadt to "read our proposal", which the UK government insists would allow about three million EU citizens to stay on the same basis as now.
EU migrants who had lived in the UK for five years would be granted access to health, education and other benefits.
But the prime minister's proposals would be dependent on EU states guaranteeing Britons the same rights.
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The leaders of the four political groups who have signed the joint letter account for two-thirds of the votes in the European Parliament.
Their letter points out that that they have the power to reject any Brexit deal before it can go ahead because the parliament must approve the withdrawal agreement.
The leaders said they would not endorse anything that removed rights already acquired by citizens.
They said the UK proposal "falls short" because it would take away rights citizens currently have, and create new red tape and uncertainty for millions of people.
The letter said this contradicted promises made by the Leave campaign that EU citizens would be treated no less favourably after Brexit.
By contrast, the letter said the EU's offer - already on the table - was simple, clear and fair because it promised that all citizens, including UK nationals living in Europe, would be treated equally and lose no current rights.
'Rights and values'
Speaking on BBC Radio 4's Today programme, Mr Verhofstadt said EU citizens in the UK - and Britons living on the continent - should keep their current rights, rather than the government "inventing a new status".
"It creates a type of second class citizenship for European Citizens in the UK," he added. "We don't see why their rights should be diminished and that would be the case in the proposal.
"In the end, it is the European Parliament that will say yes or no, and I can tell you it not will be a yes if the rights of European citizens - and also the rights of UK citizens living on the continent - will be diminished [and] cut off, like it is at the moment."
The letter stated: "The European Parliament will reserve its right to reject any agreement that treats EU citizens, regardless of their nationality, less favourably than they are at present.
"This is a question of the basic fundamental rights and values that are at the heart of the European project."
'Form-filling'
It added: "In early 2019, MEPs will have a final say on the Brexit deal. We will work closely with the EU negotiator and the 27 member states to help steer negotiations."
A spokesperson for the UK government said the letter contained a "number of inaccuracies" which could cause unnecessary and needless concern to UK and EU citizens.
Mr Green, who as first secretary of state is a close ally of Theresa May's, told BBC Radio 4's Today that it was clear that EU citizens would have to comply with "basic" immigration rules after the UK leaves the EU to establish their identity and nationality.
But he insisted: "That is not an insuperable barrier. We all fill in forms when we go on holiday and have to get visas and all that."
He suggested the UK was doing "precisely" what the EU was calling for.
"Somebody who is here now will keep the rights they already have and we hope that British citizens living in other EU countries will keep the rights they already have...The basic rights will be preserved so that should not be an obstacle to a final deal."
