The prime minister told the delegation he plans to “fight on” despite an extraordinary collapse in support that included more than 40 resignations.
Mr Johnson told ministers he was staying put, The Independent was told by a senior No 10 source, as allies made clear he would remain in place until he is forced out by another confidence vote.
His refusal to resign led to Welsh secretary Simon Hart quitting cabinet hours later, while Ed Argar resigned as junior health minister.
Mr Johnson’s aide James Duddridge told Sky News: “The prime minister is in buoyant mood and will fight on. He has a 14-million mandate and so much to do for the country.”
The Sun also quoted a key ally of the prime minister as saying: “If the party wants to overthrow the elected will of the people, they have to dip their hands in blood.”
The prime minister refused to budge despite the tally of Tory MPs who have quit his government reaching 44, in a striking symbol of power ebbing away from the man who won a stunning election less than three years ago.
Becoming the third MP to resign from Mr Johnson’s cabinet, Mr Hart wrote in his resignation letter: “Colleagues have done their upmost in private and public to help you turn the ship around, but it is with sadness that I feel we have passed the point where this is possible.”
Attorney General Suella Braverman told ITV that she would not resign but that it was “time to go” for Mr Johnson. The cabinet minister – who said she would put her name into the ring in the event of a leadership contest – said Mr Johnson had handled matters “appallingly” in recent days.
The 1922 Committee of backbenchers earlier stepped back from an immediate rule change to allow a fresh no-confidence vote – but only because it expected the cabinet to finish the job without the need for it.
The delegation was headed by Chris Heaton-Harris, the chief whip responsible for party discipline – which has broken down entirely with MPs furious about the Chris Pincher groping scandal. It included the transport secretary Grant Shapps, Mr Hart and, it is believed, Nadhim Zahawi, who was only promoted to chancellor late on Tuesday.
But Mr Johnson is believed to have told them that his departure would bring the chaos of a leadership contest during the cost of living crisis, followed by pressure for a general election.
In other conversations with wavering MPs, he urged them to recognise that, despite the mass resignations, all other potential leaders would fail to match his popularity with the public.
Earlier, in the Commons, there was applause when one Conservative MP accused Mr Johnson of attempting “to blame other people for mistakes”, telling him: “Take responsibility and resign”.
Sajid Javid, who started the mass resignations by quitting as health secretary on Tuesday evening, urged fellow Tories to follow him, saying: “The problem starts at the top and that is not going to change.”
But some cabinet ministers urged Mr Johnson to refuse to accept the game is up – forming a separate group inside No 10, in a remarkable tussle over power.
Nadine Dorries, the ultra-loyal culture secretary, pledged her continued support and, asked if it is possible he would remain in power, told reporters: “It is.”
To add to the drama, Mr Johnson broke off from the desperate fight for survival for his regular weekly telephone conversation with the Queen.
Both Kwasi Kwarteng, the business secretary, and the Northern Ireland secretary Brandon Lewis made clear they were withdrawing support from their leader.
A grim-faced Kit Malthouse, a Johnson ally since his days as mayor of London, emerged from the showdown meeting but refused to discuss what had gone on.
Some resigning ministers lashed out at the direction of the government as they left, the equalities minister Mike Freer attacking an “atmosphere of hostility for LGBT+ people”.
Rachel Maclean, the safeguarding minister, alluded to the Pincher scandal when she spoke of “heartbreaking” evidence from sexual harassment victims that “these crimes are almost always about power”.
And Mark Fletcher, an unpaid aide who witnessed the former deputy chief whip’s alleged groping of two men at the Carlton Club last week, condemned Mr Johnson’s response.
Several Tory MPs heard him blame “colleagues who were present for allowing him [Mr Pincher] to drink so much” when he toured the Commons tearoom on Tuesday, he said.
“Any person who suggests that anyone other than Mr Pincher is solely responsible for what happened that night is unfit to lead our country,” Mr Fletcher’s resignation letter read.
Mr Johnson was confronted with the news of the delegation while giving evidence to a committee of MPs, where he insisted he intends to fight on and that it is his “duty” to do so.
At an often-painful meeting of the Commons liaison committee, he failed to deny he had once said “all the sex pests are supporting me” and, of his ex-minister, “Pincher by name, pincher by nature”.
Asked “did you say he is a bit handsy?”, the prime minister told the committee: “It’s not a word I use.”
Mr Johnson insisted it would be wrong for him to resign, telling MPs he should keep governing during difficult times and refusing to “get into a running commentary on political events”.
He eventually, under fierce pressure, agreed he would not seek to call a snap general election to try to stay in power, saying: “Of course, I rule it out.”
Earlier, Keir Starmer mocked the government’s implosion, telling Mr Johnson it was “the first case of the sinking ship fleeing the rat”.
He told wavering ministers: “As for those who are left, only in office because no one else is prepared to debase themselves any longer – the charge of the lightweight brigade – have some self-respect.”
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