Government frontbencher Eric Abetz says Labor's chief Lower House strategist Tony Burke should be considering his own position, after questions were raised about his travel expenses claims.

The Coalition is searching for a new speaker after Bronwyn Bishop resigned over her use of taxpayer-funded entitlements.

Mr Burke was one of Mrs Bishop's most vocal critics, focusing on her decision to spend thousands of dollars on a helicopter trip to a Liberal party fundraiser.

Department of Finance records show in April 2012, while he was environment minister, Mr Burke made a four-day return trip from Sydney to Uluru in Central Australia and claimed his own flight worth $2,181.43 plus four "family traveller" airfares worth $8,656.48.

Tony Burke's Uluru trip His flights: $2,181.43

$2,181.43 Family's flights: $8,656.48

$8,656.48 Allowances: $1,497

$1,497 Hire car: $463.74

$463.74 Total bill: $12,707.65

Mr Burke also charged taxpayers for travel allowances worth $1,497, and $463.74 for a hire car. The total cost to taxpayers for the trip was $12,707.65.

Independent MP Andrew Wilkie is calling for an audit of all travel claims by MPs and senators dating back to 2010, and has singled out Mr Burke's use of family travel as deserving further scrutiny.

Senator Abetz has not accused Mr Burke of wrongdoing over the trip, but says the Manager of Opposition Business was pressuring Mrs Bishop to resign while having a questionable record himself.

"We have a review being undertaken as we speak, and let me just say on that I find it strange that the chief spear-thrower for the Labor Party was Mr Burke, who had to repay not once, not twice, not three times, not even 10 times, but 15 times," he said.

"I believe that Mr Burke should be considering his position given his record in relation to that area."

Mr Burke's office has released a statement saying he was on official business during the Uluru visit and held meetings "in his capacity as environment minister" with members of the nearby Aboriginal community of Mutitjulu and managers and rangers at Uluru-Kata Tjuta National Park.

"Mr Burke worked with staff including the park manager, visitor and tourism services manager, the cultural centre coordinator, media officers and senior rangers," the statement said.

"The cost of flights and the amount payable for accommodation while on official business are determined by the Department of Finance and the Independent Remuneration Tribunal, and flights are organised by the travel agent holding the Government contract."

Opposition Leader Bill Shorten said the Government was attempting to deflect the fallout from Mrs Bishop's resignation.

"You've got to love the Liberal Party don't you," he said.

"After the three weeks where the Government's gone missing, where Mr Abbott wouldn't even come out and talk to Australians about what he's doing for them, of course then they start throwing some dirt at a Labor politician."

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