Theresa May has 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", two sources present at the Conservative backbench 1922 Committee meeting have confirmed.
Tory MPs banged tables for around 25 seconds and briefly cheered as the Prime Minister arrived at the crunch meeting inside the Palace of Westminster.
It came amid suggestions from some of Mrs May's own MPs that she would have to stand down as PM after a disastrous General Election in which the Tories lost their majority and are now having to turn to the Democratic Unionist Party for support to continue governing.
One Tory MP who left the meeting midway through said there was no mood among colleagues for another leadership contest and that Mrs May spoke very well, adding "none of the Maybot".
The MP said one of the biggest cheers at the meeting came 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 in the new government.
Mr Barwell has replaced Mrs May's key aides Nick Timothy and Fiona Hill, whose resignations were reportedly demanded by Tory MPs as the price of their supporting the PM.
Mrs May also assured MPs that the DUP would not have any sway over policy on LGBT rights and any "confidence and supply" deal with them would not have any effect on talks aiming to restore the powersharing Northern Ireland government, the MP said.
Another Tory MP said there was no discussion at the meeting of how long Mrs May would remain in post, adding: "she's won, she's got to be PM".
The meeting came shortly after it was revealed that the State Opening of Parliament could be delayed beyond its scheduled date of June 19 by ongoing negotiations with the DUP to prop up her minority administration. The planned start of talks on Britain's withdrawal from the EU on the same date could also be put back.
Mrs May's most senior minister, First Secretary of State Damian 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 for the year ahead.
Senior Conservatives acknowledged that the failure to secure an overall majority in the Commons will mean the agenda set out in their manifesto would have to be "pruned back".
Details of which elements of the manifesto might be dropped have not been confirmed, but it is thought that Mrs May's poorly-received proposals for funding social care and her cherished ambition to open new grammar schools may have to be ditched.
Brexit Secretary David Davis told BBC Radio 4's Today programme: "We are being given an instruction by the British people and we've got to carry it out.
"That may mean that some elements of the manifesto will be pruned away, shall we say."
And the chair of the 1922 Committee Graham Brady agreed: "Inevitably, as we don't have a majority for the manifesto we have put forward, there will be some changes.
"The reality of this Parliament inevitably will be one of a great deal of consultation, a lot of work trying to build alliances, probably even on individual aspects of legislation, to try to pull in support from people in other parties. That might not be altogether a bad thing."
Scottish Conservative leader Ruth Davidson, who met Mrs May in 10 Downing Street 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.
"The Prime Minister is focused on getting the right deal with Brexit and I give her my full support," said Ms Davidson.
"The key issue is to ensure we put our country's economic future first and foremost in our minds as we go ahead with Brexit.
"It is clear to me that this Conservative government at Westminster is determined to deliver that."
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.
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."
There was a "huge amount of work to get on with", said Mr Green, adding: "Not just the Brexit negotiations that start next week, but many other challenges that face us and we are determined to produce a Queen's Speech to ensure we can fulfil the Prime Minister's ambition to have a country that works for everyone."
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.