Tony Abbott has laughed off the latest round of leadership talk as recycled rubbish, saying the matter was settled by the party room three weeks ago.
But talk of a second spill motion this week persists, after reports a majority of Liberal MPs and senators now want to dump him.
A relaxed prime minister poked fun at the rumours at a Clean Up Australia Day event on NSW's south coast on Sunday.
"This is Clean Up Australia Day, and I'm just not going to do anything but recycle the rubbish," he joked.
"And that's what's happening, we're just recycling rubbish today."
The party room settled the matter three weeks ago, when a spill motion was defeated 61-39, and now the coalition was getting on with governing, Mr Abbott said.
"Frankly I think the people of Australia are sick of the insider obsessions of people in Canberra," he told reporters.
Prospective leadership contenders Julie Bishop and Malcolm Turnbull steered clear of the speculation, with both declaring their support for the prime minister.
Mr Turnbull said it was "absolutely critical" Liberals concentrated on the NSW election and the return of the Baird government.
"The big political question in the next four weeks is the NSW state election," he told reporters on his Sunday morning walk in Sydney.
"The prime minister has my support. He has the support of the cabinet and life goes on."
Ms Bishop dismissed the continued rumblings as hypothetical, after News Corp reported the foreign minister would put her hand up in the event of a spill.
"The prime minister has not been challenged. There was a spill motion that didn't succeed, and what we're doing is focusing on governing," she told Network Ten.
Asked if there would be a leadership spill this week, Abbott loyalist Josh Frydenberg told ABC TV: "I hope not."
The Liberal frontbencher said Mr Abbott would never convince some MPs he was right for the top job.
"If he delivered the Gettysburg Address, if he won the Nobel Prize, they'd still take the position that they want a change in leader," Mr Frydenberg said.
He believed the prime minister should be given clear air to do his job.
"You can't please all of the people all of the time," Mr Abbott said, when asked about his colleague's comments.
"The important thing is to get on with the job of government."
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