Theresa May told Tory MPs "I'm the person who got us into this mess and I'm the one who will get us out of it", at a crunch Conservative Party meeting in Parliament, two people present have confirmed.
The Prime Minister apologised as she faced the backbench 1922 Committee for the first time since a disastrous General Election in which the Tories lost their House of Commons majority.
Mrs May also sought to reassure MPs that any confidence and supply deal with the Democratic Unionist Party (DUP) to prop up her minority administration would not affect power-sharing talks in Northern Ireland or LGBT rights.
It came as her most senior minister Damian Green confirmed that the Queen's Speech, due to set out the Government's programme on June 19, could be delayed as the Tories seek an agreement with the DUP.
The PM looks to have withstood immediate internal pressure to resign and t here was no discussion at the 1922 Committee of how long she would remain in post, although there were clear signals of how her style of rule would change to keep MPs on side.
MPs agreed that they and their constituents did not want another General Election and were united in the aim of stopping Jeremy Corbyn becoming prime minister.
Foreign Secretary Boris Johnson, who has rejected suggestions he is plotting a leadership bid, described Mrs May's speech to the '22 as a "stonking performance", adding on Twitter: "One team going forward together for the UK".
Others present said the PM gave one of her most emotional and warm speeches, with one remarking there was "none of the Maybot", while banging of the tables and cheers could be heard throughout the meeting.
There were signs that backbenchers will hold more sway, with one of the biggest cheers coming for the "greatly respected" Gavin Barwell, the PM's new chief of staff, who will have a "great deal of influence" alongside Chief Whip Gavin Williamson, according to one MP.
Ex-MP Mr Barwell replaced Mrs May's key aides Nick Timothy and Fiona Hill, whose resignations were reportedly demanded by Tory MPs as the price of their support for the leader.
Another of those present revealed that Mrs May was open to the idea of internal Tory backbench committees of MPs that would provide "seamless communication" with Number 10.
The meeting came shortly after First Secretary of State Mr Green said that agreement with the DUP would have to be sealed before finalising the details of the Queen's Speech, setting out the Government's legislative programme.
Mr Green said talks with the DUP were "going well", adding: "At this very important time, we want to produce a substantial Queen's Speech."
But senior Conservatives acknowledged that the failure to secure an overall majority will mean the agenda set out in their manifesto would have to be "pruned back".
An MP at the '22 confirmed the Tories' poorly received social care policy - dubbed the "dementia tax" - looks set to be dropped, while it is thought Mrs May's cherished ambition to open new grammar schools may have to be ditched.
Scottish Conservative leader Ruth Davidson, who attended a political cabinet meeting on Monday, said she wanted the economy to be "first and foremost in our minds" in Brexit talks, in a signal that she wants the PM to scale back her focus on her priority of controlling immigration.
"There was a real sense around the Cabinet table today, as you would expect from centre right politicians, that that is the primacy we're looking for," she told BBC News.
Ms Davidson also signalled that other parties could be more involved in negotiations.
"We do have to make sure that we invite other people in now," she said. "This isn't just going to be a Tory Brexit, this is going to have to involve the whole country."
But Mr Green said there was "complete unanimity" in the Cabinet and "overwhelming support" for Mrs May's approach.
The unexpected snap election has already forced the Queen to cancel an Order of the Garter service and to accept a stripped-down State Opening without a procession, robes or the state crown. Any further delay could mean her missing some of the races at Royal Ascot next week.
Additional delay may be caused by the fact the speech read by the sovereign is written on goatskin parchment paper, a long-lasting archival paper which contains no actual goatskin, but requires several days for the ink to dry.
A Labour spokesman said that uncertainty over the date of the State Opening showed the Government was "in chaos", while Liberal Democrat leader Tim Farron said it was "an utter humiliation" for the PM.
"It is time to stop trying to cling to power and time to admit enough is enough," said Mr Farron, who branded the possible Tory/DUP deal as a "MayDUP government".
"Theresa May can squat in Number 10 as long as she wants but the message is stark - she has no power, no influence and her game is up," said Mr Farron.
DUP leader Arlene Foster rejected suggestions that the mooted deal could undermine a return to power-sharing arrangements at Stormont, amid claims from political rivals that the Government's stated impartiality would be fatally undermined.
Mrs Foster declined to give details of what she termed a "positive engagement with the Conservative Party", but said she would be travelling to London late on Monday for discussions with her team of 10 DUP MPs ahead of a meeting with Mrs May on Tuesday.
Sinn Fein's Gerry Adams turned Mrs May's own slogan against her to brand it "a coalition of chaos", adding: "Any deal which undercuts in any way the process here or the Good Friday Agreement is one which has to be opposed."