May's deal was soundly defeated in the House of Commons this month,
Senior European lawmakers warned Thursday they will not ratify a Brexit withdrawal deal if it is stripped of guarantees on the Irish border issue.
Prime Minister Theresa May last year signed an agreement with her EU colleagues to allow Britain's orderly departure from the European Union on March 29.
But British euro sceptics objected to a so-called "backstop" in the deal that binds Britain into an EU customs union until new trading ties are agreed.
This would, in turn, guarantee that no new "hard border" would be imposed between EU member Ireland and the British province of Northern Ireland after Brexit.
May's deal was soundly defeated in the House of Commons this month, and she hopes to save it by removing or modifying the backstop to appease Conservative MPs.
EU leaders insist, however, that the withdrawal agreement is not open to renegotiation.
And now, the head of the European Parliament's Brexit steering group, Liberal group leader Guy Verhofstadt, has warned Europe would not ratify the change anyway.
In a statement, he said the cross-party group had met to discuss the latest signals from London and concluded that "the agreement is fair and cannot be re-negotiated.
"This applies especially to the backstop," he said.
"The EU remains clear, firm and united on this, even if the negotiated backstop is not meant to be used... without such an 'all-weather' backstop insurance, the European Parliament will not give its consent to the Withdrawal Agreement."
A Downing Street spokesman said Verhofstadt was "getting ahead of himself", implying the accord has not been finalized.