European Commission President Jean-Claude Juncker tweeted that the changes provide "meaningful clarifications and legal guarantees".
The backstop, a backup mechanism that would come into place if no trade deal is agreed by the end of the withdrawal period, would keep Northern Ireland in the EU's single market for goods, while the United Kingdom would remain in a customs union with the bloc. That would give her a little more time for negotiation, but it also might spell the end of her office.
At the weekend, May tried to persuade her rebellious lawmakers to back her deal when it returns to the Commons on Tuesday evening, entertaining them at her grand country house retreat of Chequers, but there were no signs that she has won them round.
British lawmakers are scheduled to vote Tuesday on whether to approve May's Brexit deal, which they resoundingly rejected in January.
The first of the votes comes tomorrow.
"We were going to have to start facing these choices this summer anyway under the prime minister's deal".
"Clearly the European Union does its utmost to complicate Britain's departure", party leader Jimmie Åkesson said last month, adding, "It would be irresponsible for Sweden to leave before knowing how it goes with Britain".
Steve Baker, a pro-Brexit member of May's Conservative Party, said the new agreement seems to fall "short" of the plan Parliament wanted to see.
If the MPs agree to extend Article 50 and therefore the negotiation process, the talks will be extended for a period of time subject to agreement with the EU.
All EU member states have to agree to an extension, and some EU leaders have expressed concern that it needs to have a specific objective.
"We remain optimistic that a hard Brexit will be avoided, and that in our view should put a floor on GBP", said Rodrigo Catril, a senior foreign-exchange strategist at National Australia Bank Ltd.in Sydney.More news: EU’s Barnier to meet UK Brexit negotiators on Tuesday
"[May secured] legally binding changes that strengthen and improve the Withdrawal Agreement and Political Declaration", Lidington said as quoted by The Telegraph newspaper.
Thirdly, Britain has put forward a "unilateral declaration" with legal status in global law emphasizing the temporary nature of the backstop, Lidington said.
Britain is due to pull out of the European Union in less than three weeks, on March 29, but the government has not been able to win parliamentary approval for its agreement with the bloc on withdrawal terms and future relations.
Media captionIs the United Kingdom actually in a crisis over leaving the EU?
The hope here is that parliament will vote in her favour and she can bring that back to Brussels in the coming two weeks to convince them to offer her concessions so that they can secure a Brexit deal.
Britain's main opposition Labour Party also came out against the agreement.
Alan Wager, a Brexit expert at the U.K.in a Changing Europe think tank, said Parliament this week could decisively rule out both May's deal and a no-deal departure.
For the Prime Minister herself, what happens this week will decide her own future.
Just 18 days before the United Kingdom is due to leave the European Union, there is still no ratified divorce deal and talks with the bloc stalled over the weekend as May felt she was unable to break the political deadlock in London.
The exact details of this vote are not yet known, including which way May will instruct her Conservative Party to vote.