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".
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"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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