Theresa May looks set to be backed by the Democratic Unionist Party as she attempts to run a minority British government following her general election disaster.
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.
The 10 MPs from the party could prove crucial in supporting the Conservatives on key votes after Thursday's election saw Mrs May lose control of the Commons.
A Number 10 spokesman said: 'We can confirm that the Democratic Unionist Party have agreed to the principles of an outline agreement to support the Conservative Government on a confidence and supply basis when Parliament returns next week.
'We welcome this commitment, which can provide the stability and certainty the whole country requires as we embark on Brexit and beyond.
"The details will be put forward for discussion and agreement at a Cabinet meeting on Monday."
A "confidence and supply" arrangement is a far looser deal than a formal coalition or pact.
It would mean the DUP backing the British government on its budget and prevent it being brought down by motions of no confidence, but could potentially lead to other issues being decided on a vote-by-vote basis.
The development comes after Mrs May sent her chief whip Gavin Williamson to Belfast for talks with the DUP after the election left the Tories eight seats short of the 326 required for a majority.
On a dramatic day, Mrs May's two closest aides Nick Timothy and Fiona Hill (both pictured) quit after coming under intense pressure from Tories following the election result.
The role of Mr Timothy and Ms Hill as Mrs May's joint chiefs of staff had been severely criticised by disgruntled Tories in the wake of the election result.
There were also misgivings about relying on the DUP, which strongly opposes same-sex marriage and abortion.
In a resignation statement on the ConservativeHome website, Mr Timothy acknowledged one of his regrets was the way Mrs May's social care policy, dubbed the "dementia tax" by critics, had been handled.
The British Prime Minister was forced to perform an unprecedented U-turn within days of the publication of the Tory manifesto by announcing there would be a cap on social care costs, something that had been absent in the original policy document.
Mr Timothy said: "I take responsibility for my part in this election campaign, which was the oversight of our policy programme.
"In particular, I regret the decision not to include in the manifesto a ceiling as well as a floor in our proposal to help meet the increasing cost of social care."
But he also set out his concerns about the way the campaign was managed, in comments viewed as a sideswipe at election guru Sir Lynton Crosby.
It said the campaign failed to get "Theresa's positive plan for the future across" or "notice the surge in Labour support".
On the same website Ms Hill said: "I have no doubt at all that Theresa May will continue to serve and work hard as Prime Minister and do it brilliantly."
Mrs May needs to shore up her position because the speech setting out the British government's programme is due on June 19, with a highly significant vote on its content expected after a few days' debate.
Mrs May called the election claiming she wanted a stronger hand in the forthcoming Brexit negotiations, due to start on June 19.
Without a majority, she could be forced to seek consensus on the approach she takes, as Scottish Tory leader Ms Davidson pointed out.
Ms Davidson, who wields considerable influence after the Scottish Tories won 13 seats, said: "I want to ensure that we can look again at issues like Brexit which we know we are now going to have to get cross-party support for.
"And move to a consensus within the country about what it means and what we seek to achieve as we leave."
In a hint that curbing immigration could become a lower priority than safeguarding the economy she said: "It is about making sure that we put free trade at the heart of what it is we seek to achieve as we leave."