While Julie Bishop says she won't challenge Tony Abbott, the prime minister could face a leadership spill next week as three coalition MPs have broken ranks and called for action.
Queensland backbench MP Warren Entsch says he'll seek to resolve festering leadership tensions when the Liberal Party has its first meeting for the year next Tuesday.
Fellow MPs Dennis Jensen and Mal Brough say the issue needs to be "lanced".
Ms Bishop assured Mr Abbott on Tuesday she was not campaigning for his job.
But Dr Jensen pointed out there didn't have to be a specific challenger for a leadership spill to be called.
The West Australian MP told Mr Abbott more than a week ago he had lost confidence in the prime minister.
"I don't think the leader and his office are listening and communicating effectively," Dr Jensen told ABC television.
"Fundamentally I see there is no strategic direction in where we are going."
Dr Jensen said many of his constituents had told him they wanted to see a change of leader.
"I believe that it is necessary that this is brought to a head and lanced," he said.
Ms Bishop, however, told Mr Abbott in a cabinet meeting she was not plotting against him.
"I am not campaigning for the job of prime minister," the foreign minister told the meeting.
"I am not ringing the backbench asking for support. I am not counting any numbers. I will not challenge the leader."
And Industry Minister Ian Macfarlane said Malcolm Turnbull, another leadership aspirant, had given his personal assurance he would not challenge.
But Mr Entsch said he strongly supported Mr Turnbull to replace Mr Abbott.
Mr Brough, a ministerial colleague of Mr Abbott under John Howard, said he couldn't offer the prime minister his unequivocal support.
"I have issues and I'm hoping to work through with the prime minister," he told reporters on the Sunshine Coast.
"The matter needs to be resolved and if Tuesday is the appropriate time for people to talk about it ... then it's for them to say so."
He personally had no intention of challenging Mr Abbott.
Immigration Minister Peter Dutton said without a leadership contender, people should back off.
"My plea is for people to give the prime minister a fair go," he told reporters in Canberra.
Mr Dutton said the backbench should get the message that Mr Abbott had unanimous support from the cabinet.
The prime minister's standing has been battered by the Prince Philip knighthood and other policy missteps, which some MPs have blamed for the Liberal National Party losing office in Queensland at the weekend.
Visiting a childcare centre in Sydney before returning to Canberra for the cabinet meeting, Mr Abbott said the lesson of Labor's leadership changes from Kevin Rudd to Julia Gillard and back again was that "instability breeds instability".
"If you want to get away from that, you just end it now and my message to the people of Australia is this is `Back to Work Tuesday'," Mr Abbott said.
Asked whether he had sought Ms Bishop's assurance about not challenging, Mr Abbott said: "Julie and I, we're friends, we are part of the leadership team. We support each other. We always have and we always will."
Treasurer Joe Hockey appeared convinced of the foreign minister's loyalty and said he'd not spoken to her or Mr Turnbull about a change of leadership.
Opposition Leader Bill Shorten said government policies were to blame for the coalition's malaise.
"The best advice I could give on behalf of Australia is drop your GP tax, drop your $100,000 degrees, drop your cuts to families and drop your cuts to pensions," he said.
An Essential poll published on Tuesday found one in four voters supported Mr Turnbull to lead the Liberals, while 21 per cent backed Ms Bishop and 11 per cent supported Mr Abbott.
Ms Bishop was the most popular among coalition voters.
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