Tony Abbott is playing down reports about the leadership intentions of his deputy as “insider gossip”.

But he’s also repeatedly refused to say whether Julie Bishop has promised not to challenge him for the country’s top job.

“I am not going to play these Canberra insider games,” he told the Seven Network.

“I think people find all that insider Canberra stuff so boring, so absolutely and utterly boring.”

Sky News reports the Prime Minister met with Bishop on Monday afternoon, where he sought a commitment that she would not run against him – a commitment she refused to give.

Asked about the claims, Bishop’s office referred AAP to her Monday comment expressing support for the prime minister.

The speculation about Bishop is another blow to the Prime Minister’s leadership, battered by the disastrous Queensland election and the Prince Philip knighthood.

Addressing questions about his plummeting popularity, Abbott said: “I never came into the parliament to be Mr Popularity.

“I came into the parliament to be get things done for the people of Australia, and that in the end is what it’s all about.”

Abbott will meet with his cabinet and wider ministry in Canberra on Tuesday to discuss the government’s agenda and priorities for the year.

Colleagues are also expected to air their concerns about his standing.

But Abbott played down the gathering as a “stock standard, start of year, cabinet meeting”.

“We will have a good talk – that’s what we do,” he said.

Treasurer Joe Hockey also dismissed reports Bishop had declined to give Tony Abbott a commitment about the leadership.

“Unsourced gossip,” he told the Nine Network.

Hockey said he’d had no conversations about a change of leadership with Malcolm Turnbull or Ms Bishop.

“If there were to be a change of leadership, it would mean, what, six prime ministers in eight years? I mean, come on.”

Labor said Bishop must resign if she cannot rule out a challenge.

“Otherwise she will be showing a gross disloyalty,” shadow employment spokesman Brendan O’Connor told Sky News.

Cabinet minister Barnaby Joyce warned unruly backbenchers against pushing for a change, saying they risked the previous Labor government’s fate.

“If you act like the Labor party you get treated like the Labor party,” he told the Nine Network.

Senior frontbencher Ian Macfarlane told reporters Bishop needed to clear the air on her ambitions.

“Talk about leadership is a distraction that needs to be put to bed,” he said.

He says Turnbull has assured him he will not mount any challenge.

Education Minister Christopher Pyne also rejected reports he could be a compromise candidate for the leadership.

“I haven’t been sounded out by anyone because I am 100 per cent supportive of the PM continuing,” he told ABC television.