Peter Dutton’s office claimed nearly $6,000 in public expenses for staff and security to travel to Perth with the opposition leader when he attended Gina Rinehart’s lavish birthday party.

Dutton’s office has said he travelled at his own expense to the party for Australia’s richest woman, which included a horseriding performance, multiple large cakes and onstage pyrotechnics. But travel information obtained under freedom of information shows members of Dutton’s team – which his office said included a staffer and a security detail – claimed travel from Melbourne to Perth and back again on 29 February, the night of the party on the banks of the Swan River.

It was reported in March that Dutton attended Rinehart’s party after the end of a parliamentary sitting week, before appearing in Melbourne the next morning to campaign for the Dunkley byelection. The Australian Financial Review reported Dutton was spotted flying from Canberra to Melbourne, then travelling on to Perth before returning to Melbourne that same evening – potentially joining Rinehart’s party for as little as an hour.

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Dutton was criticised at the time by 2GB host Ben Fordham for choosing to fly to Perth instead of spending more time campaigning in Dunkley, calling the opposition leader’s decision “a bad call” and suggested he should have “brushed” the party to campaign more in the crucial byelection.

“Peter Dutton spent more time on the aeroplane than he did at the party, which sounds like a waste of time to me,” Fordham said.

Labor’s Jodie Belyea won the byelection against Liberal challenger Nathan Conroy by a 53-47 margin.

The Independent Parliamentary Expenses Authority (IPEA), the government body which manages parliamentarians’ work expenses, released information under FoI on Thursday to show Dutton’s office claimed flights between Melbourne and Perth on the day of – and the day after – Rinehart’s party. All were classified as having been claimed by “personal staff”, rather than Dutton himself. Guardian Australia understands that any claim for Dutton himself would have been recorded and classified differently on the documents.

IPEA records show staff from Dutton’s office claimed a Melbourne to Perth flight on 29 February, the day of the party, costing $2,221.63. The same day, staff also claimed a Perth to Melbourne air fare, at $2,680.80.

The following day, 1 March, was another staff claim for a Perth to Melbourne air fare at $1,028.93.

In total, the three air fare claims between Melbourne and Perth came in at $5,931.36.

Guardian Australia contacted Dutton’s office for clarification on the claims. A spokesperson responded that the opposition leader travelled with one staff member and his security detail, which they said was appropriate and within travel rules.

Dutton is typically accompanied in public by a security detail, as are other senior politicians like prime minister Anthony Albanese and deputy PM Richard Marles.

Dutton’s spokesperson also referred back to his remarks in March, at the time of the initial reporting on his Perth trip.

“The air fares were at my expense, there was no accommodation. I flew back on the redeye so that I could be back into Melbourne at 4.30 the next morning,” Dutton said at the time.

“My security detail operates exactly the same as the governor general and the prime minister.”

The lavish celebration for Rinehart, according to her company’s websites, included “a horse show backed by the fantastic Aussie music, The Man from Snowy River, with riders … carrying large Australian and company flags”.

The Perth lord mayor, Basil Zempilas, told 6PR radio he attended the event, calling the horseback show “an incredible sight”, and saying the pop star Guy Sebastian had sung the national anthem.

Last year Dutton was flown to another Rinehart party at Hancock Prospecting’s Pilbara mine by another billionaire rich-lister, where he praised the mining magnate and her family as “pioneers” who had “given so much to this country”.

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