Talks since have focused on the "backstop," which is created to keep the Irish border open but which critics say could indefinitely lock Britain into a customs union with the EU.
It was unclear to what extent the offer would help May in her attempt to push the withdrawal agreement past her parliament next Tuesday.
In her speech in the pro-Leave stronghold of Grimsby, the Prime Minister urged MPs to back her Withdrawal Agreement, warning the country could be plunged into crisis - and Brexit derailed altogether - if it is rejected.
"It needs just one more push, to address the final specific concerns of our Parliament", she said.
He said the EU was also ready to give "legal force" to reassurances given to Mrs May concerning the operation of the backstop in January in a joint letter from European Council president Donald Tusk and European Commission president Jean-Claude Juncker.
It came as May delivered a speech created to persuade MPs to back her Brexit deal when it is put to a vote on Tuesday.
May acknowledged that, even if her deal passes next week, time will be tight to pass the necessary legislation needed to make Brexit a reality on March 29. The Democratic Unionist Party, which is based in Northern Ireland and props up Ms.
In contrast, 245 lawmakers openly oppose the idea, 15 are deeply skeptical and a further 94 government ministers and whips, or parliamentary enforcers, would be required to vote in line with the government's position against another referendum. The Tory rebels and DUP want a time limit put on it or changes made that would allow the U.K.to unilaterally withdraw from it.
Lawmakers across parties cite worries about prolonging uncertainty and increasing division as reasons for opposing a vote, while the most common argument is that it would be undemocratic to seek to overturn the result of a vote in which more than 30 million people took part.
Attorney General Geoffrey Cox has been in Brussels this week trying to persuade the European Union to alter the arrangement, which Brexiteers say could trap the United Kingdom into abiding by European Union rules without a say in them.
Why is Brussels smiling? Irish Prime Minister Leo Varadkar said the British, not the European Union, had to compromise, and the decision to leave the bloc had been "a problem of their own creation". They say the backstop is essential because it upholds the 1998 Good Friday Agreement that ended decades of sectarian violence in Northern Ireland and eliminated all border controls, and they argue that inserting a time limit would defeat its goal. "They have failed to secure ratification of this so it should be a question of what they are now willing to offer us", Varadkar told journalists in Dublin. May's pitch. "To be clear: we are running out of options", he told reporters on Friday.
The Tory rebels are giving little ground as well, with some indicating that Ms.
But while Tuesday's votes on amendments are not binding on the government, they would be politically hard to ignore. "Logic suggests if you ask the same question then you get the same answer".