"We have worked as a party with the DUP before and those are productive talks".
"That means we need to proceed with the maximum possible consensus and that we also need to make sure that the concerns of people who voted Remain, many of whom now actually want us to press ahead with leaving the European Union as quickly and as in as orderly fashion as possible, but we need to make sure that their concerns are part of our conversation".
Mrs May is also engaged in delicate negotiations with the Democratic Unionist Party (DUP), a small Protestant party from Northern Ireland that usually plays no role in British-wide politics, but whose 10 MPs are now crucial to the survival of the May government.
Mrs May addressed a packed meeting of the 1922 Committee for 90 minutes after her failure to win the election outright prompted days of speculation about her future. There was no need for a general election, she insisted, until she changed her mind.
"She said 'I'm the person who got us into this mess and I'm the one who is going to get us out of it, '" said one Conservative lawmaker who attended.
However, the German finance minister Wolfgang Schaeuble said it was not too late for UK.to change its mind. She said calls for Mrs May to go had "faded" but her authority was "extremely fractured".
"The form of the DUP in the past in the past, and the type of policies that they have put forward, the type of policies that they have pursued with the Tories in the past, are very very concerning", Pearse Doherty, a Sinn Fein lawmaker in the Irish parliament, said.
The danger for the Conservatives is that the longer Mrs May clings on, the more she alienates the electorate, and the more attractive an opposition Jeremy Corbyn becomes.More news: Kansas governor vetoes $1.2B income tax increase
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London has said it wants formal political talks between Barnier and Brexit minister David Davis to start next Monday but it since Thursday's election it has not formally committed to the date.
Brussels has warned that time is running out to start the talks on divorce terms and a future trade deal, with Britain set to leave the European Union come what may in March 2019.
From across the Channel, Michel Barnier, the EU's chief negotiator, urged Britain not to delay Brexit talks.
She denied that a DUP-Tory deal would undermine the Good Friday Agreement and the chances of a return to devolution at Stormont.
While Britons voted by 52 to 48 percent for Brexit in last year's referendum, Scots strongly backed staying in the bloc and Nicola Sturgeon, First Minister in Scotland's devolved assembly, said a so-called Hard Brexit was "dead in the water".
It comes as the party has accused the DUP of betraying the interests of Northern Ireland by agreeing to prop up a Conservative minority government.
After two hours of negotiations at No 10, the DUP's leader, Arlene Foster, has remained in London for further talks.
Northern Ireland has been without a powersharing executive since March and without a first and deputy first minister since January. "Conducted in the right way it can be how we resolve our differences, how we deal with injustices and how we take, not shirk the big decisions". We recommended that she make use of Gavin Barwell. Davis, who said that some policies in the government's programme would now be pruned back, was one of a number of senior Conservatives to publicly pledge loyalty to May.
Foreign Secretary Boris Johnson, who is also touted to replace Mrs May should she be forced out, wrote in The Sun newspaper that people "have had a bellyful of promises and politicking", and that "now is the time for delivery - and Theresa May is the right person to continue that vital work". The Evening Standard, edited by ex-Treasury chief George Osborne, reported that Cabinet ministers have initiated talks with Labour lawmakers to come up with a "softer", less hard-line divorce from the EU.