The moves buy May a temporary reprieve.
A spokesman for 10 Downing St has confirmed that the DUP are said to be "happy" with the outline of a deal proposed to them by Theresa May.
May is expected to form the new government after talks with the DUP next week, only days before the country's historic Brexit negotiations with the European Union start on June 19.
Then, after midnight, Downing Street responded, saying: "The Prime Minister has tonight spoken with the DUP to discuss finalising a confidence and supply deal when Parliament returns next week. We have more in common with them than we do the other parties".
Ms May called the snap election to win a clear mandate for her Brexit plans, so she could slash immigration.
The Conservatives won 318 out of 650 seats - throwing away a 17-seat majority.
Labour, the main opposition party, won 262.
Late on Saturday, she appointed a new chief of staff, former housing minister Gavin Barwell who lost his parliamentary seat in last Thursday's election.
All in all, it was a mistake on Mrs May's part to call a general election, when she had plenty of time to govern with a reasonable majority.
Conservative legislator Nigel Evans said the departure of the two aides was "a start", but there needed to be changes to the way the government functioned in the wake of the campaign.
Clearly, the general election result was a huge disappointment. "Our manifesto was full of fear and the Labour Party's manifesto was full of promises".
"I suspect we'll have something different coming in a couple of weeks time".
It added that "the logic leading to Mrs".
Chants echoed around Downing Street of the new alliance, with organisers from the Stand Up to Racism and Stop the War speaking to the angry crowds. Beleaguered May is appointing new members of her government after several.
The DUP will not stand for any arrangement that physically sets the region apart from anywhere else in the United Kingdom, including suggestions that border, immigration and customs controls could be set up at ports and airports like Stranraer and Liverpool rather than in Belfast or Larne.
It risks upsetting Northern Ireland by aligning London closely with the pro-British side in the divided province, and increases the chance that Britain will fall out of the European Union in 2019 without a deal.
"It is quite possible there will 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", Mr Corbyn, who has called on Ms May to resign over the election result, told the BBC.
Mrs. May is due to meet with the 1922 Committee on Tuesday evening after meeting with DUP leader Arlene Foster.
"I could not care less what people get up to in terms of their sexuality. It is quite possible she will go".
The Labour leader, who survived an attempt to oust him by his own MPs before the election, now expects that he will be able to attract some of the party's biggest names to serve on his front bench.
Newspaper headlines saw her as just clinging on.
Ukip wants Brexit to remain the PM's focus.
Ruth Davidson, out-lesbian leader of the Scottish Conservative Party warned May to keep the DUP in line.