The moves buy May a temporary reprieve. "That's not a matter for me", she said.
Late Saturday both Downing Street and the DUP issued statements saying talks over a deal to prop up the government would resume next week, amid concern among more liberal Conservatives about May hitching her wagon to the right-wing Northern Irish party. That means the DUP would back the government on confidence motions and budget votes, but it's not a coalition government or a broader pact.
None of the parties got a majority in the House of Commons.
The Conservative Party has depended on Irish politicians before: Prime Minister John Major relied on support from the Ulster Unionist Party to shore up his shaky government in the mid-1990s.
In Thursday's election, the DUP won 10 of Northern Ireland's 18 seats in the 650-member British parliament.
Labour leader Jeremy Corbyn said she had lost all legitimacy and called on her to stand aside and allow him to form an alternative administration, declaring: "We are ready to serve".
Foster said Friday it would be "difficult" for May to continue in her role. A "soft" Brexit, by which the United Kingdom gets to stay in the single market and European Union citizens can remain in the United Kingdom, now seems more likely but that will require a great deal of horse-trading.
"It was a disaster", he said.
The Labour Party was crippled by in-fighting and defections.
Martin Selmayr, senior aide to European Commission President Jean-Claude Juncker, responded to the resignations by tweeting the word "bauernopfer" - German for the sacrifice of a pawn in chess.
British Foreign Secretary Boris Johnson has denied plotting to topple Prime Minister Theresa May, who has been weakened by the Conservative Party's disastrous election result. She's now attempting to form a government.
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Failure in the talks could lead to a return to direct rule from London for the first time in a decade, and fuel tensions that have in the recent past led to street violence and attacks by dissident nationalists. "May sought a mandate".
Johnson had been a favorite to win the keys to Number 10 after Cameron quit, but he pulled out of the race.
The socially conservative, pro-British and largely Protestant party finds itself in the unlikely position of possible kingmaker.
Defending her party's stance on gay marriage in a recent interview, leader Arlene Foster insisted those who characterised the DUP as anti-gay were wide of the mark.
Money for Northern Ireland will undoubtedly be part of their demands, and Mrs May will expect that.
"I could not care less what people get up to in terms of their sexuality".
A third sign, inspired by Theresa May's election slogan, said: "As strong and stable as my sign".
Initial talks have begun with Northern Ireland's DUP after Mrs. UKIP leader Paul Nuttall resigned after just six months in the job, following his party's dismal performance.
MP Anna Soubry, a popular Conservative "Remainer", told the BBC's Andrew Neil that May is "set to go in due course" and that her position is "untenable". "May fights to remain PM", said the front page of the Daily Telegraph, while the Times of London said: "May stares into the abyss".
But I think the Conservative Party thought actually, the alternatives to Theresa May staying in place were even worse.
"I don't think throwing us into a leadership battle at this moment in time, when we are about to launch into these hard negotiations, would be in the best interests of the country", Evans said.