The Conservative Party should "get its house in order", back Theresa May and "let her get back to governing", the party's leader in Scotland has said.
Ruth Davidson criticised Tory "plotters" who want the PM to resign, saying they should "put up, or shut up" and were not led by anyone "serious".
Former party chairman Grant Shapps says about 30 Tory MPs back his call for the party to hold a leadership contest.
But the prime minister said she has the "full support of her cabinet".
Speaking on Friday, she insisted she was providing the "calm leadership" the country needed.
Pressure on the prime minister has grown since her party conference speech was plagued by a series of mishaps, as she struggled with a persistent cough and was interrupted by a prankster.
Mr Shapps, who was co-chair of the party between 2012 and 2015, said he believed it was "time we actually tackle this issue of leadership" adding that "so do many colleagues".
However, cabinet ministers including Environment Secretary Michael Gove and Home Secretary Amber Rudd were among those who backed the PM on Friday.
And speaking on Radio 4's Political Thinking podcast, Ms Davidson, leader of the Scottish Conservatives, suggested the prime minister's critics should "put up, shut up and get off the stage".
"I have to say, I've not got much time for them," she said of Mrs May's critics, saying there were "an awful lot of people in our party who need to settle down".
"I think if the plotters were serious, they would be led by someone a bit more serious," she said.
"One of the irritants over the last couple of days, for me, particularly as a woman, is this idea that all of these men are supposed to be making decisions on Theresa May's behalf," she added.
"Well, have they actually met Theresa May? This is a woman with agency, with grit, with determination. I backed her in the leadership, I back her now and I will back her in the future."
Asked what she would say to her party, she added: "I would tell my party to get its house in order.
"Get together, knuckle down and make sure our first commitment, our last commitment and our only commitment is to the country we are incredibly lucky to serve."
To trigger a vote of confidence in the party leader, 48 of the 316 Conservative MPs would need to write to the chairman of the backbench 1922 committee.
A leadership contest would only be triggered if Mrs May lost that vote, or chose to quit.
Mr Shapps said no letter had been sent and that his intention had been to gather signatures privately and persuade Mrs May to stand down.
But he claimed party whips had taken the "extraordinary" step of making it public by naming him as the ringleader of a plot to oust the PM in a story in the Times.
He added: "The country needs leadership. It needs leadership at this time in particular.
"I think the conference and the lead-up through the summer has shown that that's not going to happen. I think it's time that we have a leadership election now, or at least let's set out that timetable."
Former minister Ed Vaizey was the first MP to publicly suggest Mrs May should quit on Thursday, telling the BBC: "I think there will be quite a few people who will now be pretty firmly of the view that she should resign."