May, however, insisted her party was still in pole position to lead, despite falling short by eight seats, CNN reports. "We want to do it quickly, respecting the calendar", she said in comments reported by Sky News.
Chancellor Philip Hammond, Foreign Secretary Boris Johnson, Home Secretary Amber Rudd, Defence Secretary Michael Fallon and Brexit Secretary David Davis have all been kept on in their roles.
The news came as May prepared to name the rest of her cabinet, after revealing on Friday that her five most senior ministers would remain in their posts.
Former Treasury chief George Osborne - who was sacked by May past year - called May a "dead woman walking", and Labour leader Jeremy Corbyn said he was ready to contest another election at any time.
This was likely to involve an arrangement in which the DUP would support a Conservative minority government on key votes in Parliament but not form a formal coalition.
Theresa May's party lost the majority they had and are now reaching out to a socially conservative party called the Democratic Unionists to try to form a government.
Beard: Well, I suspect not Jeremy Corbynm because Jeremy Corbyn is sitting very pretty now on the sidelines. The result was a hung Parliament, with no party big enough to form an overall majority. With negotiations over leaving the European Union in 10 days' time, the prospect of internal political wrangling is causing concern in Brussels.
A source close to the DUP said the party was seeking more funding for the province and concessions for former British soldiers in exchange for supporting May. "I blame her party for destroying Britain by pushing for Brexit and austerity, two things that will ultimately be bad for my generation".
The Labour MP for Nottingham East refused to say whether he thought Mr Corbyn was credible prime minister.
In a night that redrew the political landscape once again, the UK Independence Party (UKIP) - instrumental in campaigning for Brexit - lost millions of voters, prompting its leader Paul Nuttall to quit.
"What tonight is about is the rejection of Theresa May's version of extreme Brexit", said Keir Starmer, Labour's policy chief on Brexit, saying his party wanted to retain the benefits of the European single market and customs union.
"The mandate she has got is lost Conservative seats, lost votes, lost support and lost confidence", he said. Many analysts said it was unlikely May could remain leader for long now that her authority has been eroded.
"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.
Sky gave similar estimates to Lord Ashcroft of how young people voted, showing that 63 per cent of 18- to 34-year-olds voted Labour and 27 per cent Conservative.
But there is one area where the DUP could exert real influence: Brexit, where the party has pushed for a softer line than May herself, partly to guard against the possibility that Northern Ireland and the rest of Ireland would be too deeply severed - with the north cut out of the European Union and the rest staying in.
Instead, her election gamble has failed and she and her Conservative party have been weakened, with many on Friday questioning May's future as prime minister. Within hours, President Donald Trump launched an insensitive Twitter tirade against the mayor of London, a member of the Labour Party.
Apple Showcases New iMac Pro Workstation at WWDC
If you plan to do some serious typing, spreadsheets, and video editing, the Microsoft Surface Pro will give you more mileage. Aside from the display size, one of the physical features that's most noticeable is the new screen technology.
Russia interfered in US elections, says James Comey
The complaint from Kasowitz will focus on Comey's testimony before the Senate Intelligence Committee Thursday morning. Comey's Capitol Hill testimony is one of the most prominent congressional hearings in years in Washington .
Patty Jenkins is ready for the 'Wonder Woman' sequel
Her chance to accomplish her goal arrives when she rescues Steve Trevor, a spy who almost drowns when Germans tie him to a boat. In Wonder Woman , audiences learn about Themyscira and the culture of the Amazons through Steve's curiosity and questions.