Video report by ITV News Political Correspondent Carl Dinnen
The Prime Minister has told Conservative backbenchers she will get them "out of this mess" after the party saw their majority wiped out at the General Election.
Theresa May told the influential 1922 Committee: "I'm the person who got us into this mess, and I'm the one who will get us out of it."
Sources who attended the meeting said Mrs May apologised several times over the Tory MPs who lost their seats following the June 8 election.
They continued that the Prime Minister apologised to backbenchers following the election result and told them: "I'll serve you as long as you want me."
One MP said Mrs May "showed her human side" during the meeting, something which "happened far too rarely during the election campaign".
They added that the Prime Minister said she would learn the lessons of the General Election campaign, particularly that voters wanted more money spent on public services, highlighting schools, hospitals and childcare in particular.
The MPs continued that the committee was in agreement with the Prime Minister that another General Election or a party leadership election will not be held in the foreseeable future as they are "the last thing the country needs".
An MP who attended the meeting said their was no discussion of how long Mrs May would remain as leader of the Conservatives, since "she's won, she's got to be Prime Minister".
Despite the Conservatives losing their majority at the election, the committee members banged the tables for around 25 seconds and briefly cheered as Mrs May arrived at the meeting inside the Palace of Westminster.
Chair of the 1922 Committee, Graham Brady, echoed these reports, stating that there remains "really solid support" within the party for Theresa May.
Mr Brady told how it had been a "great meeting" and the "Prime Minister had judged the mood and the tone exactly right...
"She rightly took responsibility both for calling the election and for the campaign that was so unsuccessful in delivering the outcome we had all hoped for.
"But she also set out some of the reasons why it's critically important in the national interest that we should do the responsible thing and form a government and try to provide some resilience and effectiveness in government."
Mr Brady voiced his support for Mrs May who he said had been a "good" and "effective" Prime Minister.
The 50-year-old said that Mrs May's lead in opinion polls before the General Election was called indicated this, but added the Prime Minister's campaigning in the run-up to June 8 had not been such a success.
However, Mr Brady continued that Mrs May is now "back to running the Government as Prime Minister and that in itself will help to build the longevity of the Government".
Mrs May met the committee amid suggestions from some Conservative MPs that she would have to stand down following the disastrous election result which has resulted in the Tories seeking support from the [Democratic Unionist Party (DUP) to prop up their Government.
However, Mrs May assured MPs 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 power-sharing Northern Ireland Government.
Mr Brady said an alliance with the DUP could help to create an "effective, reliable, stable government".
However, an alliance with the DUP would "inevitably" lead to a "slimmed down" Queen's Speech, Mr Brady said.
The MP for Altrincham and Sale West continued: "Of course there were things in the manifesto that many of us would have liked to take a good, hard, fresh look at again in any case - I'm thinking of policies like the social care policy - but there may have been all sorts of others things that would not have commanded majority support in this House of Commons.
"We've got to be realistic, there's no point in soldiering on and introducing swathes of legislation which aren't going to be passed by the House of Commons, so I think it will be a slimmer Queen's Speech and will take a deal of care and pragmatism to get there."
One of the biggest cheers during the meeting came for the "greatly respected" Gavin Barwell, Mrs May'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 who both stepped down after facing furious criticism from party MPs and officials who said they played a significant role in the party's poor performance at the General Election.
The resignations were reportedly demanded by Tory MPs as the price of their supporting the Prime Minister.
It was revealed on Monday that Mr Timothy and Ms Hill are both in line for payouts of around £35,000, as under government rules, they are entitled to severance pay equivalent to three months' wages.