Prime Minister Tony Abbott says he encourages Malcolm Turnbull's ambition for the top job.
Mr Abbott last week survived a spill motion 61-39.
It was widely believed the communications minister would have stood for the Liberal leadership if it had been declared vacant.
"I encourage it," Mr Abbott told Sydney radio station Triple M of Mr Turnbull's ambition.
The prime minister didn't agree with broadcasters the former Liberal leader was "breathing down his neck".
"I wouldn't characterise it as that," he said.
"I would say that what Malcolm is doing is his job and he's got a very important job in the government."
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