Labor’s chief lower house strategist Tony Burke has hit back at Government criticism of his decision to charge taxpayers more than $12,000 for a trip to Uluru with his family.

At the time Mr Burke was the environment minister and his office said the visit to Central Australia involved official business, including meetings with managers and rangers at the Uluru Kata Tjuta National Park and members of the nearby Aboriginal community of Mutitjulu.

Mr Burke claimed travel allowances for his return flight between Uluru and Sydney, and four “family traveller” airfares.

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He also claimed other costs for car hire and expenses.

The overall claim for the trip was $12,707.65.

Mr Burke maintains the travel claims were within the rules but he is facing pressure from some sections of the Government over the spending.

Government frontbencher Eric Abetz said Mr Burke should consider his position.

Parliamentary secretary to the Prime Minister Alan Tudge echoed those concerns, describing it as “classic Labor hypocrisy” for Mr Burke to criticise outgoing speaker Bronwyn Bishop over her use of entitlements.

Assistant Treasurer Josh Frydenberg also called Mr Burke a “hypocrite” amid further reports on Wednesday he claimed travel to go to a Robbie Williams concert last year.

“I don’t know how he can justify charging the taxpayer to go to a Robbie Williams concert… next he’ll tell us he has portfolio responsibilities for shadowing Kim Kardashian,” Mr Frydenberg told Sky Television.

But the Prime Minister was not prepared to add his voice to the criticism when he was questioned about the trip at an Adelaide media event.

“On particular members of Parliament and whether particular spending was good, bad or indifferent, I just want to say the important thing is to get the rules right,” Tony Abbott said.

Mr Burke has released a statement arguing there is a distinction between his actions and Mrs Bishop’s claims.

“My criticism of Bronwyn Bishop was that she had broken the rules,” he said.

“Today’s articles explicitly acknowledge that there is no allegation that I have broken any of the rules at any point.”

Mrs Bishop has repeatedly denied the suggestion that her entitlements claims, including the helicopter charter for a Liberal fundraiser, were in contravention of the rules.

The Department of Finance is now investigating her spending.

– ABC