She said that she would seek "legally binding" agreements for any new deal but admitted negotiations would not be easy.
She will whip MPs to support the amendment tabled by 1922 Committee chairman Sir Graham Brady, which states that Parliament would be willing to support the Withdrawal Agreement reached with the European Union if "alternative arrangements" were found to avoid a hard border.
Downing Street said the PM remains committed to quitting the European Union on March 29 and will take her plan back to the Commons for a second "meaningful vote" as soon as possible after Tuesday's debate.
At the same time, Labour lawmaker Hilary Benn has put down a proposal for lawmakers to hold a number of "indicative votes" to find out which option the House of Commons was the likeliest to support, while Conservative Andrew Murrison is urging for the backstop to either end by December 2021 or be scrapped from the withdrawal agreement.
She said alternatives to the backstop had been "extensively discussed at the negotiating table".
"This Withdrawal Agreement has been agreed with the United Kingdom government, is endorsed by leaders, and is not open for renegotiation", the European Commission spokesman told the journalists.
"I hope that our friends in Brussels will listen and that they will make that change", he said.
It's far from certain that the amendment will win support from a majority in the House of Commons when it comes to a vote later Tuesday.
Labour said it was supporting the amendment because the bill it would create could "give MPs a temporary window to agree a deal that can bring the country together".
Weber said: "If there is now a unilateral attempt to reopen the agreement, the effect will be that not just the backstop has to be renegotiated - then the Gibraltar question, the question of how much money Britain has to pay for exiting, the question of citizens' rights will have to be renegotiated".
Senior Brexiteer Sir Bernard Jenkin said he did not intend to back it, telling ITV News: "It's very vague and it's deliberately vague because it's meant to mean different things to different people".
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British Prime Minister Theresa May had urged lawmakers to support the move and "tell Brussels that the current nature of the backstop is the key reason Parliament can not support this deal".
"But what we need is to achieve something legally binding. We can't have some codicil or letter or joint declaration".
Indeed, EU officials were quick to reject any renegotiation.
She said such a change would not be easy and there was "limited appetite" on the part of the European Union, but she believed she could secure it.
"That's why I think now Article 50 should be extended, there should be a request made for that and the SNP were the first party to call for that". The Graham Brady amendment gives conditional approval, so that is an issue.
Former Foreign Secretary Boris Johnson, who resigned previous year in opposition to the backstop and May's agreement, described the amendment's passage as "a victory for the prime minister, but also it's a victory for the U.K." as it allows May to return to Brussels stronger to negotiate changes.
Plaid Cymru's Liz Saville-Roberts said "chasing unicorns is not a plan". The prime minister backed this amendment late Monday to increase its chances. At some point there has to be compromise on all sides in order to get a deal over the line.
With more than a dozen amendments tabled, many by cross-party groupings of MPs, the outcome will depend on which ones are selected for voting by John Bercow.
However, Britain could not leave the backstop without the EU's consent. We have to look for ways to do that.