"The prime minister has tonight spoken with the DUP to discuss finalizing a "confidence-and-supply" deal when Parliament returns next week", a spokesman said early on June 11.
The unionist party's leader told Sky News she plans to act in the national interest, saying: "We want to do what's right for the whole of the United Kingdom".
British media reported that moves were afoot within May's Conservative Party to dislodge her, while opposition Labour leader Jeremy Corbyn, who exceeded expectations in Thursday's vote, called for her to go and said he could form a government.
While the to-and-fro between Downing Street and the DUP was unfolding, several British newspapers were reporting that some prominent Conservatives, including Foreign Secretary Boris Johnson and Brexit minister David Davis, were being urged by supporters to challenge May for the party leadership.
"To those that say the PM should step down, or that we need another election or even - God help us - a second referendum, I say come off it. Get a grip, everyone", he wrote in an article for The Sun. But not for some time, let's get this clear.
The Conservatives secured 318 seats in the 650-seat House of Commons - just short of the 326 seats needed to control a majority.
In a further bid to win over disillusioned lawmakers, May appointed Michael Gove, a long-serving cabinet minister with whom she has clashed in the past, as environment minister while two of her closest aides, who many blamed for the election result, resigned.
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Depending on the device you are watching from, you may need to go over to YouTube to see the new Forza video in 4K at 60 FPS. We'll also be going hands-on with the Xbox One X in the next couple of days, as E3 2017 gets fully underway.
The spokesman indicated this would not be a formal coalition but a minority government with loose DUP support on a "confidence and supply basis". She has kept in place her broader team of ministers too, with only a few changes.
Ms Foster said: "We had very good discussions yesterday with the Conservative party in relation to how we could support them in forming a national government - one that would bring stability to the nation and those discussions continue".
May's office said on Saturday principles of an agreement had been reached but the two sides later clarified that they were still talking.
The exact contours of a potential Conservative-DUP deal were not yet known. The DUP is a socially conservative group that opposes abortion and same-sex marriage and had links to Protestant paramilitary groups during Ireland's sectarian "Troubles".
The Prime Minister was doing her utmost to signal that it was business as usual, announcing that she would be heading off to Paris on Tuesday for talks with French president Emmanuel Macron.
A separate YouGov poll for the Sunday Times found that Corbyn is now neck-and-neck with May on who the public believe would make the best prime minister.
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