Mrs May failed to win a majority in parliament at the election last week, prompting calls for her plan to leave the EU's single market to be watered down, and for some rival lawmakers to demand that the Brexit process be delayed.
Sinn Fein has warned such a move undermines power-sharing talks in Northern Ireland and the party's seven MPs have flown to London where they will hold a briefing with reporters.
A week after May lost her majority in an election she had called in the hope of strengthening her hand in the talks, some fellow Conservatives want her to focus more on limiting the damage to business and less on cutting immigration and other ties to the European Union when Britain leaves the bloc in March 2019. But speculating now on different kinds of trade pact - on "soft Brexit" or "hard" - is to put cart before horse, they say.
"We stand at a critical time with those Brexit negotiations starting only next week - I think that stability is important".
DUP leader Arlene Foster has said she is keen to secure a "frictionless" border with Ireland and has spoken out against a "hard Brexit".
But one MP present at the meeting said there was no discussion of a leadership contest, adding "she's won, she's got to be prime minister".
Mrs May needs the votes of the DUP's 10 MPs to prop up her minority administration as she hopes to steer government business - including crucial measures on Brexit - through the Commons.
She is correct of course to adopt that approach, for she knows that expectations are high back at home that she can wrest significant concessions from the Prime Minister given her once-in-a-lifetime position of leverage.
Death toll rises to 17 in London high-rise fire
A tower once home to hundreds of people is now a blackened husk, looming over a neighborhood in grief. Rydon, the firm responsible for the refit, said the project "met all required building regulations".
A senior Conservative Party source said the talks were ongoing.
Mrs May's Conservatives unexpectedly lost their majority in parliament in Thursday's snap general election, causing political chaos ahead of Brexit talks with the European Union set to start next week and prompting calls - from within her own party - for her resignation.
He will meet with Michel Barnier, the EU's chief negotiator, on Monday.
His comments come after Emmanuel Macron, the new French President, said alongside Theresa May at the Elysee Palace that the "door remains open" if the United Kingdom ditches its Brexit plans.
Downing Street said Cabinet ministers had discussed the Government's legislative programme when they met earlier but refused to be drawn on discussions about plans to deal with the DUP.
As six senior Conservatives argued for closer links between Britain and the European Union they also said Labour and other parties should have a say in the final deal.
"We would restore faith in politics if we could show that this parliament can at least function in presenting a view in the national interest which would command a majority on a cross-party basis", said veteran pro-European Conservative lawmaker Ken Clarke. "The risk is that Northern Ireland continues to fail to find solutions, and potentially the peace process unwinds", Usherwood said.
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