The prime minister,Tony Abbott, has praised Labor’s support for military intervention in Iraq, distancing himself from his treasurer, Joe Hockey, who questioned the value of bipartisanship on the issue when the opposition would not pass the budget.

As Australia carried out its first air strike on an Islamic State target in Iraq, Hockey demanded that the federal opposition pass the budget in order to allow the government to meet the costs of the conflict, expected to run to hundreds of millions.

But during a morning radio interview, and at a press conference later on Thursday, Abbott declined to endorse Hockey’s remarks, pointing instead to co-operation between the major parties on the Middle East conflict to date.

Labor however moved to capitalise on Hockey’s untidy intervention. The Labor leader, Bill Shorten, said the prime minister should “correct his treasurer”.

“Joe Hockey probably thought he was being clever, creating this political issue. Well it’s not,” Shorten said in Melbourne. “Every time Joe Hockey opens his mouth now he says something silly.”

“Australians will see through this political game. Under no circumstances should our intervention in Iraq be used as a source to justify hurting Australian people through this unfair budget – and the cuts and raised taxes which flow from it.”

Shorten went to a matter of policy contention within the Coalition: declaring that if the government needed additional resources to fund Australia’s military operations, it should dump the prime minister’s signature paid parental leave scheme.

Coalition MPs have continued to speak out against the generous scheme – arguing the money would better be directed elsewhere.

“Why don’t they actually go after the multinationals they’ve gone soft on?” Shorten said “There are plenty of measures that this government could do if it really is the crisis that Joe Hockey says it is.”

Hockey had told reporters in Washington that the costs associated with Australia’s military intervention were another reason Labor should “immediately pass the remaining measures in the budget”.

“Everything comes at a cost and if Bill Shorten truly is honest about his commitment to deliver bipartisan support in relation to our defence efforts in the Middle East he’ll provide bipartisan support to pay for it,” he said.

Earlier in the week, the finance minister, Mathias Cormann, declined to rule out raising taxes to pay for the conflict, but the prime minister stepped in on Tuesday to do so.

Abbott, speaking on Fairfax Radio on Thursday, would not link passing the budget and paying for the Iraq contribution, despite being given several opportunities to do so by his host, Neil Mitchell.

Abbott said Shorten had been a “patriot” on Iraq, and had been concerned to address the threats posed by Islamic State.

On the subject of the budget, the prime minister said it remained incumbent on Labor to suggest alternative savings or revenue measures to ensure long-term fiscal sustainability if the opposition did not like the government’s approach. Abbott also accused Labor of playing politics on unpopular measures such as the GP co-payment.

At a media event later in the day, Abbott said: “What is important is that the opposition continues to support our mission in Iraq and the Middle East.”

“Obviously there’s a lot of things that the government and the opposition disagree [about] but when it comes to national security it’s good that we stand shoulder to shoulder together.”