Theresa May's grip on power appears far from secure despite a proposed deal with the Democratic Unionist Party to support her in Parliament.
Downing Street said an outline agreement on a "confidence and supply" arrangement had been reached with the DUP which will be put to the Cabinet for discussion on Monday.
But the strength of that deal looks set to be tested when the Commons meets next week, with Jeremy Corbyn vowing to try to bring down the Government by defeating Mrs May in Parliament and insisting: "I can still be prime minister."
In another sign of the dangers facing Mrs May, Sunday papers reported that Boris Johnson was being encouraged to make a leadership bid in an effort to oust her, or actually preparing one - a claim dismissed as "tripe" by the Foreign Secretary.
The 10 DUP MPs could prove crucial in supporting the Conservatives on key votes after Thursday's election saw Mrs May lose control of the Commons.
A "confidence and supply" arrangement is a far looser deal than a formal coalition.
It would mean the DUP backing the Government on its Budget and confidence motions, but could potentially lead to other issues being decided on a vote-by-vote basis.
Mrs May needs to shore up her position in Parliament because the Queen's Speech setting out the Government's programme is due on June 19, with a highly significant vote on its content expected after a few days' debate.
The Labour leader told the Sunday Mirror he would oppose the Queen's Speech all the way.
"I can still be prime minister. This is still on. Absolutely," Mr Corbyn said.
Meanwhile sources close to the Foreign Secretary dismissed reports about his leadership ambitions as "complete bollocks" and suggested "someone is trying to make mischief".
The Mail On Sunday reported that Mr Johnson was preparing a leadership bid, with a a close ally saying it was "go, go, go", adding: "We need Bojo."
Mr Johnson said: "Mail on Sunday tripe - I am backing Theresa may. Let's get on with the job."
But the Sunday Times said Mr Johnson had been pressed by five Cabinet colleagues to oust Mrs May.
An ally of Mr Johnson told the newspaper: "We are facing a populist and they have realised we need someone who can talk to the people.
"We need a Brexiteer. Boris is the only option with the liberal values, Brexit credentials and popular appeal."
A spokesman for Mr Johnson said: "The Foreign Secretary is 100% supporting the PM and working with her to get the best deal for Britain."
The potential deal with the DUP came after Mrs May sent her Chief Whip Gavin Williamson to Belfast for talks after the election left the Tories eight seats short of the 326 required for a majority.
In other developments:
:: Mrs May's two closest aides Nick Timothy and Fiona Hill quit after coming under intense pressure from Tories following the election result.
:: Ex-minister Gavin Barwell, who lost his seat in Thursday's election, was named as the new chief of staff, replacing Mr Timothy and Ms Hill.
:: Scottish Tory leader Ruth Davidson indicated she wanted to see a fresh approach to Brexit by seeking a consensus across parties.
:: A former minister said Mrs May must not be allowed to lead the party into the next election.
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 regrets over the way Mrs May's social care policy, dubbed the "dementia tax" by critics, had been handled.
But he also set out his concerns about the way the campaign was managed, in comments viewed as a side-swipe at election guru Sir Lynton Crosby.
The campaign failed to get "Theresa's positive plan for the future across" or "notice the surge in Labour support".
In her statement, 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 called the election claiming she wanted a stronger hand in the forthcoming Brexit negotiations, due to start on the same day as the Queen's Speech.
Without a majority, she could be forced to seek consensus on the approach she takes, potentially by performing a U-turn on single market membership, protecting the economy at the expense of immigration controls.
Ms Davidson, who wields considerable influence after the Scottish Conservatives 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 at the approach she wanted, 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."
The Sunday Times reported that Chancellor Philip Hammond used a telephone call with Mrs May on Friday to tell her she should put jobs first in the Brexit negotiations - a coded attack on the immigration-focused strategy.
A DUP spokesman said discussions with the Tories would continue next week.
The talks were in line with leader Arlene Foster's "commitment to explore how we might bring stability to the nation at this time of great challenge", the party said in a statement.
It continued: "The talks so far have been positive. Discussions will continue next week to work on the details and to reach agreement on arrangements for the new Parliament."