Speaking during a trip to Japan, she said a Brexit agreement was still possible, but first "we must hear from Great Britain how they envision that". It has so far refused to put a legally-binding time limit on it.
Anger has centred on Mrs May's call for fresh negotiations with Brussels over the contentious Irish backstop plan.
"Parliament's mandate is to replace the backstop".
"The current backstop, as I have said all along, is toxic to those of us living in Northern Ireland", DUP Leader Arlene Foster, who will meet May in Belfast on Wednesday, told BBC Radio.
"We want to reach a deal which can provide certainty for business but that also is in the long-term interests of Northern Ireland".
The Republic of Ireland is Northern Ireland's largest market, accounting for 31 percent of its total exports in 2016, which is 2.1 percent of the UK's GDP.
Theresa May dropped three hints on Tuesday in Belfast that her Plan A to get a Brexit deal through Parliament is to tweak/seek reassurances to the controversial backstop in the Withdrawal Agreement that was roundly rejected by MPs in January, rather than find a replacement.
She added that, with just unionists represented in the Commons, it is more important than ever to ensure that the rights of all in Northern Ireland are respected.
Hundreds call for help as floodwaters continue to rise in Townsville
Townsville resident Chris Brookehouse told national broadcaster ABC his house was flooded with water that was more than 1m deep. Boats are launched from a road to help evacuate flood-affected people from Townsville on February 4, 2019.
He added that the Good Friday agreement can not be used as a bargaining chip while Brexit advocates search for an alternative arrangement.
The EU has repeatedly ruled out removing the backstop and the prime minister herself has insisted that any withdrawal deal must include it in some form.
'The UK government will not let that happen, ' she said.
As a way to prevent a hard border, Brussels and London agreed a so-called backstop - basically a promise that unless the sides come up with a better idea, then the United Kingdom would remain bound by European Union market and customs rules so that goods would not have to be checked.
"We know the only way to do that is the issue of the backstop, the backstop which Theresa May and her Government negotiated with the EU".
The revelation follows weeks of uncertainty around Brexit negotiations, with the UK Parliament rejecting Prime Minister Theresa May's Withdrawal Agreement and then voting for her to reopen negotiations over a controversial Irish "backstop", meant to avert a hard border between Britain and European Union member-country Ireland in future.
The Prime Minister's official spokesman said that various "streams of work" are being investigated and commented: "All of those are being taken forward urgently".
"The Prime Minister can keep stressing her commitment to the Good Friday Agreement and to avoiding a hard border, but unless she has a coherent and realistic plan those warm words don't amount to much", he said.
The SDLP, Sinn Fein, Alliance and the Greens and the Labour Party in Northern Ireland - who all backed Remain in 2016 - want alterations to the backstop.