Speaking during a visit to Northern Ireland, the prime minister confirmed she would be seeking changes to the insurance policy, which is designed to prevent a hard border reforming on the island of Ireland (Other OTC: IRLD - news) if a trade deal cannot be struck in time.
Mrs May restated her "unshakeable" commitment to avoiding a hard border post-Brexit, pledging: "The UK government will not let that happen. I will not let that happen."
The PM acknowledged the importance of a seamless border, saying it had helped "deliver peace and prosperity".
The two-day trip comes ahead of her visit to Brussels on Thursday, with Mrs May hoping to reopen her withdrawal agreement during talks with Jean-Claude Juncker and Donald Tusk.
In a question and answer session after a speech in Belfast, the PM was asked how she could convince people in Northern Ireland to accept a deal which had no backstop.
Mrs May replied: "I'm not proposing to persuade people to accept a deal that doesn't contain that insurance policy for the future.
"What parliament has said is that they believe there should changes made to the backstop.
"And it is in that vein, in that light, that we are working with politicians across Westminster, across the House of Commons, but also will be working with others - with the Irish government and with the EU - to find a way that enables us to maintain our commitments that we have set, very clearly, for no hard border, but to do it in a way that provides a Withdrawal Agreement and Political Declaration for the future that can command support across the House of Commons and therefore that we will be able to ratify with the EU such that we leave on March 29 with a deal."
Challenged on whether she had made a U-turn on the backstop, the PM said: "There is no suggestion that we are not going to ensure that in the future there is provision for this - it's been called an insurance policy, the backstop - that ensures that if the future relationship is not in place by the end of the implementation period, there will be arrangements in place to ensure that we deliver no hard border."
Mrs May's deal was overwhelmingly rejected by MPs last month, but last week they supported an amendment calling on her to get the backstop replaced with "alternative arrangements".
The options being considered by the government include a unilateral exit mechanism, a time limit to the backstop, swapping it for a free trade agreement and potential technological solutions.
There are some within Mrs May's party who want it scrapped altogether, so the PM's latest comments are likely to cause disquiet among Leave-supporting MPs.
And Jo Stevens, a Labour MP and supporter of the Best for Britain campaign for a second referendum, said: "The prime minister might have a decent speechwriter, but her actions always speak louder than her insincere words.
"The opportunity to prevent a hard border is there for her to take if she rules out no deal. Instead she continues to bend to Brexit extremists in her party who deny the importance of the Good Friday Agreement."
DUP leader Arlene Foster, who will hold talks with Mrs May during her visit, told Sky News it was "vitally important" that the backstop was replaced.
She (Munich: SOQ.MU - news) said: "She [Mrs May] now has a very clear mandate from the House of Commons. I want her to take that clear mandate and clear message to deal with the backstop and to deal with the problems that have arisen because of the backstop being in the withdrawal agreement.
"It's vitally important that we replace that backstop, that we deal with it. Because currently it creates a hard border between Northern Ireland and the rest of the United Kingdom and that's totally unacceptable."
Sinn Fein accused the PM of serving up little more than "platitudes and promises" with "nothing new" in her words in Belfast.
Party vice president Michelle O'Neill said: "I heard no words of comfort, no assurances, I heard nothing that would leave the community here to be in any way in a better position than from before her visit."
Opponents of the backstop fear it will weaken the constitutional integrity of the Union - as Northern Ireland would be treated differently to the rest of the UK by following different rules and regulations.
Fears have also been expressed that Britain could end up being trapped in the arrangement - and by extension the EU - indefinitely.
The EU and Ireland have insisted on the need for a backstop - and Ireland's deputy prime minister Simon Coveney dismissed the idea of "alternative arrangements" out of hand last week.