But it later disclosed that no deal had been finalised and talks on the arrangement will continue during the week as Mrs May desperately tries to shore up her position after losing her Commons majority in the election.
Downing Street said an outline agreement on a "confidence and supply" arrangement had been reached which will be put to the Cabinet for discussion on Monday.
DUP leader Arlene Foster said she would meet May on Tuesday while Downing Street said the incumbent premier would "finalize" a deal in the coming week.
Britain's Prime Minister Theresa May and her husband Philip walk into 10 Downing Street, in London, Britain June 9.
If May is to honor the wish of the 52 percent of voters who opted a year ago to take Britain out of the European Union, she must find a way to bridge the differences within her party.
German Chancellor Angela Merkel, meanwhile, said Friday that she's ready to defend the interests of European Union members in exit negotiations and doesn't see any reason for the process to be delayed by the results of the U.K.'s election.
Speaking on the BBC's Andrew Marr show, Mr Corbyn said: "We're going to put down a substantial amendment to the Queen's Speech which will contain within it the main points of our manifesto, and so we'll invite the House to consider all the issues we put forward which I've mentioned - jobs-first Brexit, mention the issues of young people and austerity, there's many other things".
He told the Sunday Mirror: "I can still be prime minister". A senior Conservative lawmaker, Gavin Williamson, was in Belfast for talks with the party on Saturday, a spokeswoman for May's office said. Some say her failure means the government must now take a more flexible approach to the divorce.
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Most of his rivals were in trouble as they turned for home but Tapwrit emerged from just off the pace with a strong challenge. Tapwrit wore down Irish War Cry to win the Belmont Stakes for Todd Pletcher.
A spokesperson for the Prime Minister has declined to comment on the timing of any talks between the two parties. The Conservatives could command a thin majority with the support of the DUP if they manage to to do a deal with the Northern Irish party.
According to media accounts, internal pressure on May led to the resignation on Saturday of the Prime Minister's two co-chiefs of staff, Nick Timothy and Fiona Hill, who have been blamed for their role in designing the Conservatives' campaign and the parliamentary setback.
Ultimately, the DUP are economic populists and parochial in outlook, and the wishlist they present to the Conservatives is likely to be dominated for requests for more United Kingdom government funds for Northern Ireland, although a UK-wide repeal of the bedroom tax was one of the demands they presented in 2015. She's then got to present a programme to parliament, ' he said.
May has said Brexit talks will begin on June 19 as scheduled, the same day as the formal reopening of parliament.
Asked if she was a "strong and stable leader" just 36% agreed and 50% disagreed.
The nursery worker said he was "angry" that Mrs May had done a deal with the DUP, although he admitted he did not initially know who they were. She's taking us back to those times.
The best-selling Sun newspaper said senior members of the party had vowed to get rid of May, but would wait at least six months because they feared a leadership contest could propel the Labour party into power under Jeremy Corbyn, who supports renationalisation of key industries and higher taxes for business and top earners.
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