The European Parliament's lead Brexit negotiator Guy Verhofstadt has rejected Theresa May's offer on citizens' rights, claiming it was casting a "dark cloud" over people's status.
In a joint article with a cross-party group of senior MEPs, Mr Verhofstadt said the Prime Minister's plan was a "damp squib" which carried a risk of creating "second-class citizenship".
The MEPs said the European Parliament had the ability to reject any deal that eroded the rights currently enjoyed by EU citizens.
They also made clear they would block any attempt to extend the two-year deadline for Brexit, saying it was "simply unthinkable" for the process to drag on.
The difficult issue of the rights of EU citizens in the UK - and Britons on the continent - is one of the first tasks facing negotiators in the Brexit talks.
In a sign that MEPs could veto any Brexit deal that did not meet their demands, they said: "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."
Mrs May's plan would allow EU nationals resident in the UK to apply for "settled status" - effectively guaranteeing them indefinite leave to remain in the country once Britain is out of the bloc.
Any EU citizen who has been living in the UK continuously for five years can get the status, while those who have been resident for less than that period will be also be allowed to stay and then apply for settled status once they have clocked up the necessary time.
Dependent family members - children or parents - who join an EU national in the UK prior to Brexit will also be able to apply once they have been in the country for five years.
After Brexit, EU citizens with settled status will be able to bring family members from overseas on the same terms as British nationals.
The MEPs said there were "striking" differences between the UK's offer and that set out by the EU's chief negotiator Michel Barnier who "wants British people and Europeans to keep the same rights and the same level of protection they currently enjoy".
The UK's offer "was a damp squib, proposing that Europeans obtain the status of 'third-country nationals' in the UK, with fewer rights than British citizens are offered throughout the EU".
The MEPs also insisted the European Court of Justice should play a "full role" in enforcing citizens' rights - something which is a red line to Mrs May.
They said: "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."
While they want an "ambitious and progressive" withdrawal agreement, they stuck to the EU's position that sufficient progress on issues including citizenship and the UK's divorce bill has to be made before talks on a future relationship can begin.
The added: "Brexit negotiations must be completed by March 30, 2019; we will not support any extension to this deadline, because it would require the UK to hold European elections in May 2019. That is simply unthinkable."
Nicholas Hatton, who co-chairs the3million group which supports EU citizens in the UK welcomed the intervention and urged the Government to show "pragmatism" and offer the "same level of protection" the EU had.
He said: "EU citizens in the UK will appreciate that MEPs are standing up for our rights while the current British Government has decided to play politics with our lives."