It was a humiliating outcome after an election that May had planned to strengthen herself ahead of the Brexit push.
The Conservatives won 318 out of 650 seats - throwing away a 17-seat majority. As May struggled to contain the fallout, her two closest aides resigned.
However, there have been serious doubts on the stability of such a government and May's own leadership of the Tory party. But Johnson said he backed May.
"I told her that there were a number of things that count to me more than the party".
The details of the agreement "will be put forward for discussion and agreement" at a cabinet meeting on Monday, a day before the new parliament meets, the spokesman said.
That said May had "spoken with the DUP to discuss finalising" a deal in the coming week.
Still, the deal with the DUP risks upsetting the political balance in Northern Ireland.
But the wooing of the DUP risks upsetting the political balance in Northern Ireland by aligning London more closely with the pro-British side in the divided province, where a power-sharing government with Irish nationalists is now suspended.
The source said the DUP was likely to seek a role in Brexit negotiations but was likely to steer clear of social issues such as abortion and gay rights, where it disagrees with Conservative Party positions.
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German Chancellor Angela Merkel said she assumed Britain still wanted to leave the European Union and talks should start quickly.
However, the Conservative Party were only 287 votes from forming a majority government and could have done so by winning four seats.
So what does it want, and how will this change Brexit?
She put on a fearless face, refusing to show any contrition for the election gamble that spectacularly backfired, but observers say she has been deeply wounded.
The pound on Friday fell 1.7 and 1.4 percent against the United States dollar and the euro, respectively.
May emphasized toughness on terrorism, especially after recent attacks in Manchester and London, but proved to be an uninspiring campaigner who refused to take part in televised debates with her opponents.
Fallon also said he believed there was a majority in parliament for this Brexit plan. She confirmed this to German leader Angela Merkel in a phone call on Saturday.
He said the Conservative election manifesto - which Hill and Timothy were key in drafting - was "a full assault on the core Tory voters, who are senior citizens".
Britain's typically right-wing press savaged May over the election outcome, questioning whether she will be able to remain in power after a result that leaves her reliant on uniting rival factions within her party to deliver Brexit.
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May's chief of staff Nick Timothy , left, and Joint-chief of staff Fiona Hill leave the Conservative Party headquarter on Friday. The losses complicate the SNP's plans to push for a new referendum on Scottish independence as Britain prepares to leave the EU.
Opposition Leader Jeremy Corbyn said he thought there could be another election soon, after the vote on Thursday produced no clear victor and left Ms May under pressure from her own backbench and allies.
With media asking questions about whether May could remain at Downing Street after her electoral humiliation, ministers said now was not the time for the further uncertainty that a party leadership contest would bring.
Last night former leadership contender Chuka Umunna said he would be happy to serve in a Shadow Cabinet to help Labour "get back into government" in a sign any rebellion was now over.
May had repeatedly ruled out the need for a new election before changing her mind.
"This is still on", he said, adding he would vote down the government's programme when it comes before parliament this month.
The alliance makes some modernizing Conservatives uneasy. If she is to succeed in delivering the wishes of 52% of the public and take Britain out of the European Union, she must find a way to secure the full support of her party to pass legislation preparing for and enacting the departure.
Its eurosceptic wing has always been a thorn in the side of Conservative prime ministers. The main opposition Labour Party took 262.
"Imagine she survives until autumn of next year", he said. Davidson also said she had received reassurances from May that the party's deal with the DUP would not involve a rollback of gay rights.
Johnson dismissed the reports as "tripe", tweeting late on Saturday that he was backing May.
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Varying testimonies suggest Constand had between one and a half and three pills, which would range from 37.5 to 75 milligrams. His lawyers also declined to disclose their strategy or say who will testify when they begin presenting their case.
And over a cappucino he says it is time for Mrs May to wake up and smell the coffee.