Tory MPs have rallied round Theresa May after her conference speech on Wednesday was marred by mishaps.
James Cleverly said he was "proud" of the PM for contending with a persistent cough and a prankster and John Redwood said MPs backed her "strong message".
However, it is thought dozens of MPs are discussing the possibility of trying to persuade Mrs May to stand aside.
But it is not clear whether they will have enough support to move.
In the keynote address in Manchester - billed in advance as Mrs May's opportunity to assert her authority after her decision to call a snap election backfired and amid continuing Brexit divisions within the party - she apologised to activists for her shortcomings during this summer's campaign.
She put forward a range of new policies, including an extra £2bn to build 25,000 new council houses and social homes for rent by 2021 and draft legislation for a cap on standard tariff energy bills, which she said were part of her mission to improve people's lives and promote a "British dream".
PM struggles through interrupted speech
May revives promise to cap energy prices
Security review after PM pranked
Could May have fixed her croaky voice?
However, the aftermath of the speech was dominated by the prime minister's struggle in delivering it and questions about what it meant for her future.
A nagging cough and croaky voice forced the PM to almost stop on more than one occasion but she sought to make light of her troubles, cracking a joke when Chancellor Philip Hammond handed her a cough sweet.
A succession of cabinet ministers, including Boris Johnson, Michael Gove and Jeremy Hunt, praised the speech afterwards.
A Number 10 source confirmed it had received calls from colleagues "offering support" to the prime minister and declared "resignation is not an issue" for Mrs May.
Politics is certainly cruel, and clearly the prime minister was the victim of some appallingly bad luck.
A former minister told me that after the election and Grenfell it would only have taken one more event to trigger her exit and this "was the event".
In normal political times, it is probably the case that what one minister described as a "tragedy" would have led to a prime minister being forced out or quitting.
But these aren't normal times. Allies of Theresa May say Wednesday's events have shown her resilience and determination in spades, demonstrating exactly why she deserves to stay in the job.
Mr Redwood, a former minister in John Major's government, said Mrs May had a "lot more to give" in her role and that in discussions with colleagues after the speech he detected a "lot of warmth and support for her".
"I and many Conservative MPs like me are fully behind her and we are sorry for her that her voice went at the wrong moment," he told the BBC.
"We don't think that tells us very much about what she is going to do for the country which is what really matters. People feel, as I do, that it is a pity that her big day was spoilt by those two things.
"But we do not think it spoils the underlying message and the strong point she made to the party that it is our job to get on delivering a strong Brexit."
Tory MP Nadhim Zahawi said the PM had shown her "grit and determination" in the face of adversity and "of course" would stay on as leader.
"When she gets a good deal from our Euro partners the whole narrative will change," he told Channel 4 News. "She is focused and will deliver."
Security at future Conservative events is to be reviewed after a comedian was able to get within yards of the prime minister and hand her a mock P45 redundancy notice.
Prankster Simon Brodkin - also known as his TV persona Lee Nelson - was arrested by Greater Manchester Police after briefly interrupting the PM and giving her a sheaf of paper he claimed was from Boris Johnson.
He was later released, with the police saying he had "legitimate accreditation" to attend the event.
To add to Mrs May's woes, some of the letters fell off the conference stage backdrop behind her during the speech. By the end it read: "Building a country that works or everyon."
Labour seized on the confusion, publishing a spoof image on social media suggesting their opponents had run out of ideas, while also criticising Conservative housing and energy policies as limited and timid.
And former Conservative deputy chairman Lord Ashcroft said there was an air of a party that did not "know what it is doing".
"One thing the week needed to do was take a step towards restoring the Conservatives' reputation for competence," he wrote on Conservative Home. "On that front, unfortunately, there is a way to go."