Michel Barnier, the EU's chief Brexit negotiator, indicated on Twitter that the European Union was prepared to show some patience, making it clear that talks should not begin until the political situation had settled in the UK.
Ms May has faced calls to resign following the Conservatives' disastrous performance at the ballot box which left the party with 318 seats - 8 short of a majority - after a much-criticised campaign which saw a seemingly unassailable lead gradually diminished.
May's new chief of staff will be Gavin Barwell, a former MP who was ousted from his south London constituency as a result of Labour's unexpectedly strong showing in the election.
Brexit negotiations are due to begin on Monday June 19, and Theresa May has maintained that the talks will go ahead as planned despite the political turmoil.
She also told the BBC that she sought assurances from May that the Tory approach to gay rights will not change if the party enters into an agreement with the DUP.
"We will put forward a position in which we negotiate tariff-free access to the European market and legislate after that", he added.
The arrangement with the DUP will make governing easier, but it makes some Conservatives uneasy.
UAE: Qatar fueling row by courting Turkey, Iran
It said hackers installed a file and then published a fake news item attributed to Sheikh Tamim just after midnight May 24. That crisis end eight months later, but the roots of it are clearly seen in the latest dispute.
In Ireland, there is growing concern that by bringing the DUP into government, London will no longer be able to perform its traditional role as an impartial broker in the Northern Ireland peace process. "There has been a lot of hyperbole about the DUP since Thursday", Foster said. We've only just scratched the surface here. "We don't want the DUP demanding money for this or that project they fancy every time we need them to support us in a vote".
Asked if she thought Mrs May would be able to stay in her job, the DUP leader told the BBC: "I don't know", adding: "I think it will be hard for her to survive". "I think we'll know very shortly".
Speaking to Geo News, protestors said that Jeremy Corbyn has changed the way politics is done in Britain.
After an initial round of discussions, Downing Street had said on Saturday that the "principles of an outline agreement" had been agreed with the DUP. It was tough enough when she had her own majority.
"We're a year now since the referendum".
As the June 8 poll ended in a hung parliament, with no party holding an absolute majority in the House of Commons, Mrs May pledged the Tories would offer "stability" as the largest party with the most votes.
The result has demolished May's political authority, and she has also lost her two top aides, sacrificed in a bid to save their leader from being toppled by a furious Conservative Party. J.K. Rowling, the prominent author of the Harry Potter series of novels, predicted past year that Corbyn would bring about "the destruction of the Labour Party". "I'm sure many of them will want to vote for government measures needed to execute our departure from the European Union".
She said Labour had to be ready for another election "at any time" and warned the party not to "rest on its laurels", saying it had to work on how to win back more seats from the Conservatives.
Newspapers said foreign minister Boris Johnson and other leading party members were weighing leadership challenges. "Without it, I don't see how we govern with any confidence".
"I think its quite possible there'll be an election later this year or early next year, and that might be a good thing, because we can not go on with a period of great instability", he told the BBC's Andrew Marr on Sunday.
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