Prime Minister Tony Abbott has dodged a barrage of questions about whether Foreign Minister Julie Bishop refused to offer him assurances she would not challenge for the leadership.

Speaking on Channel Seven’s Sunrise program on Tuesday morning, Mr Abbott said he would not play “Canberra insider games” when questioned about whether he had asked Ms Bishop not to challenge.

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“I meet with Julie Bishop all the time… the public elected me as Prime Minister to end Labor’s mess. We’re not going to go back to the chaos of the Labor days,” Mr Abbott replied.

When Sunrise host David Koch asked Mr Abbott to confirm or deny the allegations, the prime minister said he didn’t want to be drawn into “insider gossip”.

The comments come after Sky News alleged Mr Abbott had met with Ms Bishop and asked her not seek the prime minister’s position.

On Tuesday morning, Industry Minster Ian Macfarlane called on Ms Bishop and Communications Minister Malcolm Turnbull to assure Mr Abbott they would not challenge him.

Both are seen as frontrunners for the prime minister’s position.

“We need to get on with government and talking about the leadership is a distraction that needs to be put to bed,” Mr Macfarlane told reporters.

“I’d call on both Malcolm – who I know is not planning any leadership challenge because he gave me that assurance – but I would also call on Julie Bishop to make that assurance.”

Sky News said Mr Abbott met with Ms Bishop on Monday afternoon and sought a commitment she what would not run against him.

The ABC also said it had confirmed Mr Abbott sought such an assurance from Ms Bishop, but it wasn’t given.

While promoting his childcare policy in Sydney on Tuesday morning, Mr Abbott said he would not be calling a spill.

“Julie and I are friends, we’re part of the leadership team, we support each other, we always have and we always will,” he said.

“I have a lot of confidence in my colleagues. I have a lot of trust and faith in them.”

The prime minister also warned that “instability breeds instability”.

“If you want to get away from instability you just end it now.”

Speaking on Tuesday morning, Treasurer Joe Hockey dismissed reports of Ms Bishop’s refusal to not challenge as “unsourced gossip”.

“I say to others in the party – focus on the jobs of everyday Australians rather than your own. That’s what matters,” Mr Hockey said on Channel Nine.

Cabinet minister Barnaby Joyce also warned backbenchers against calling for a leadership spill.

“If you act like the Labor party, you get treated like the Labor party,” Mr Joyce said.

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

His cabinet colleagues are likely to air the concerns about the prime minister’s leadership.

But Mr 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.

“We will be a strong, determined, united government working as hard as we humanly can for the people of Australia.”

– with AAP