This is not the time to be changing leader, Armed Forces Minister James Heappey has argued, as he defended the prime minister, reports BBC.
Suggestions that there is a candidate to replace Liz Truss who would unite the party is "for the birds", he added.
Ms Truss has insisted she will lead the Conservatives into the next general election, despite U-turns leaving her battling to salvage her authority.
Labour is calling for an election regardless of Ms Truss's position.
Speaking the the BBC's Political Editor Chris Mason, Ms Truss apologised for the mistakes she made over the ill-fated mini-budget.
On Monday, Chancellor Jeremy Hunt reversed almost all of the tax-cutting proposals laid out last month by former Chancellor Kwasi Kwarteng.
The prime minister chaired a meeting of the Cabinet on Tuesday morning, and is also expected to hold talks later with the European Research Group of Tory MPs, who are on the right of the party.
And Ms Truss has been holding meetings with her cabinet ministers and backbench MPs as she tries to reassure her party.
But there is deep unrest in the Conservative Party and active debate about whether and when to try and get rid of the prime minister, with some MPs believing it is urgent and she should be removed as soon as possible.
One former cabinet minister said: "Whatever happens, it has to happen soon."
Other MPs believe the prime minister has bought herself some time with the appointment of Mr Hunt and the dumping of the growth plan, and are waiting to see what further measures the chancellor outlines in a further economic statement on 31 October.
Mr Heappey said the public "will not indulge the Conservative Party tearing itself apart" with another change of leadership.
"We have seen over the past two or three weeks what the economic price of political instability has been," Mr Heappey added.
Speaking to BBC Breakfast he admitted the mini-budget was "unhelpful".
He said "dozens" of his Tory MP colleagues are "gravely concerned" but "they like me recognise this is not the time to be changing leader again".
And speaking to Sky News, Mr Heappey also said that "given how skittish our politics are" at the moment "I don't think there's the opportunity to make any more mistakes".
Labour's shadow chancellor Rachel Reeves told BBC Breakfast the "only thing left from the prime minister's plan is higher mortgage rates and higher bonuses for bankers".
She said the prime minister "can put herself and all of us out of this misery by resigning and calling a general election".
A YouGov poll on Tuesday has found that Ms Truss favourability rating has fallen to -70. Just one in 10 Britons have a favourable opinion of the prime minister, according to the poll.
Budget U-turns
On Monday, Mr Hunt announced that nearly all the tax cuts announced at last month's mini-budget would be scrapped.
And he said the government's energy support package - a policy repeatedly championed by Ms Truss in defence of her premiership - will be reduced from April.
Former Cabinet minister Andrew Mitchell said Conservative MPs should recognise "the best possible answer for good government" is to make sure leadership under Ms Truss and Mr Hunt works.
"They are now working together in tandem and I think that arrangement has got to be given the chance to work" he said.
"If it's not a success and it doesn't work then the Conservative parliamentary party will have to think again."
Five Conservative MPs have publicly called for her to resign.
Some Tory MPs are talking privately about how Ms Truss could be ejected from office, despite party rules preventing a formal leadership challenge for a year.
At a meeting of the centrist One Nation Tories, several MPs called for a cabinet reshuffle.
Following the meeting, MP Simon Hoare said: "If there was a seriousness about a resetting and a recalibration then there would have to be a reshuffle."
One MP described Ms Truss's meeting as "the first time I have heard a corpse deliver its own eulogy".
An unknown number of MPs have sent in letters to the 1922 Committee, which represents backbenchers and which controls the rules surrounding Tory leadership contests.
Some hope that if more than half of MPs told committee chair Sir Graham Brady they want the prime minister to go, he would make it clear to her.
One person who backed Ms Truss for leadership agreed she was unlikely to lead the party into the next election, but said: "You're often defined by what your opponents can't do", meaning that if the plotters can't agree, the PM will stay in place.
There appears to be little agreement over who should take over from Ms Truss if she was removed.
Defence Secretary Ben Wallace has quashed rumours that he could replace Ms Truss should she resign.
Speaking to the Times, he said he will be holding on to his current job and accused Tory MPs of playing "political parlour games".