The Conservatives remain in talks with the DUP in a bid to form a partnership that would see Mrs May able to push through a legislative programme.
Anger in May's ranks is palpable, with some prominent members uncomfortable with the plan to form a parliamentary alliance with the pro-Brexit DUP.
May shrugged off suggestions her days in Downing St. were numbered.
But rumors swirled of plots to oust May.
However, pressure is growing among Tory MPs for the foreign secretary, Boris Johnson, to challenge May for the leadership.
The 10 DUP MPs could prove crucial in supporting the Conservatives on key votes after Thursday's election saw May lose control of the Commons, reports the Press Association. Labour surpassed expectations by winning 262.
Former Tory leader Lord Hague said "very serious lessons" had to be learned by the party but warned against a leadership contest.
Many senior Conservatives say May should stay, for now, to provide stability.
May confirmed the appointments of many of her leading ministers, with only a few tweaks including the promotion of ally Damian Green to Cabinet Office minister, a senior role that administers the day-to-day running of the government.
While Mrs May is set to be allowed to govern, she will have to go by the time of the next election, he said.
She called the early election with her party comfortably ahead in the polls in the hope of increasing her majority and strengthening Britain's hand in exit talks with the European Union. Instead, she has left Britain's position in disarray, days before the divorce negotiations are due to start on June 19.
This is not the approach adopted by the PM, who plans to withdraw from the single market and customs union and bring net migration below 100,000.
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Fifth-seeded Elina Svitolina advanced to the French Open quarterfinals by beating Croatian qualifier Petra Martic 4-6, 6-3, 7-5. Nishikori beat Murray in a dramatic five-setter 1-6, 6-4, 4-6, 6-1, 7-5 a year ago to reach the semifinals at Flushing Meadows.
Defence Secretary Michael Fallon, one of May's most loyal supporters, said he disagreed with Osborne's description of her as a "dead woman walking" and he expected Conservative lawmakers to rally behind her.
An ally of Johnson told the newspaper: "We are facing a populist and they have realised we need someone who can talk to the people".
"If any of that is a condition of confidence and supply it simply won't work".
DUP leader Arlene Foster told Sky News she would meet May on Tuesday.
Many senior DUP figures admire not only Mrs May's forthright unionism but her brand of One Nation Conservatism and her move away from some of the stridently individualistic Thatcherite rhetoric.
The deal sits uneasily with some Conservatives because of the DUP's opposition to abortion and same-sex marriage.
A supply and confidence arrangement is not a formal powersharing coalition.
SCULLY: Well, the Democratic Unionists are a party which strongly believes in Northern Ireland continuing to remain within the United Kingdom.
Irish Prime Minister Enda Kenny tweeted Sunday that he had spoken with May "and indicated my concern that nothing should happen to put (the Good Friday Agreement) at risk".
The DUP is now engaged in a negotiations after the collapse of the power-sharing administration that runs the Northern Ireland Executive.
"We are going to put down a substantial amendment to the Queen's Speech which will put forward the points in our manifesto", said Corbyn. Adding insult to the injury, her speeches became riddled with sound bites, such as strong and stable leadership, which ultimately turned into political boomerangs to haunt her throughout the campaign.
May spoke to the Irish Taoiseach (Prime Minister) Enda Kenny over the phone on Sunday. "This is still on".