The federal government wants the independent expenses watchdog to provide advice on overhauling travel perks for MPs, opening the door to changes after a backlash over politician’s entitlements.

The opposition leader, Sussan Ley, is prepared to work with Anthony Albanese to reform the system, offering a truce after a week of damaging headlines about MPs’ largesse.

The health minister, Mark Butler, said the government would “welcome” the Independent Parliamentary Expenses Authority (IPEA) widening its probe of Anika Wells’ travel claims to include recommendations about the system overall.

If IPEA recommended legislative changes, Butler told Sunrise on Friday: “I’m sure that’s what we would do”.

The government could immediately change the rules for politicians’ travel through regulation or legislation given parliament, not IPEA, has responsibility for the rules.

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But the comments from one of Albanese’s closest political confidants confirm the government is open to changes to the entitlement system, bowing to public pressure after the backlash to revelations about parliamentarians’ travel spending.

Wells this week referred her own expenses to the watchdog for audit on Wednesday amid a torrent of damaging stories about her claims, starting with a near $100,000 travel bill to spruik the social media ban in New York in September.

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What are the family travel rules?

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Politicians in Australia can claim nine business class airfares for their spouse to travel from their home city to Canberra each year, according to the parliamentary expense authority, the IPEA. Politicians can also claim three economy fares per child.

For places outside of Canberra, however, politicians can claim three return business class airfares for family members in total.

IPEA’s website says: “Family reunion travel can be accessed where: the parliamentarian is travelling for the dominant purpose of conducting parliamentary business, and; the family member/s travels to accompany or join the parliamentarian, and; travel is for the dominant purpose of facilitating the family life of the parliamentarian"

IPEA conducts reviews of parliamentarians’ travel expenses, making findings on whether the specific expenditure is consistent with the rules.

However, those reviews do not make recommendations about the system overall.

Guardian Australia has sought clarification from the special minister of state, Don Farrell – who has ministerial responsibility for IPEA – whether the government has specifically instructed the watchdog to broaden the scope of its audit of Wells’ expenses.

Politicians embroiled in the growing expenses scandal – including Wells, Albanese, Don Farrell and others – have defended their use of the family travel rules to bring their spouses and children to events such as the Australian Open and major NRL and AFL matches, saying it was within the rules.

Guardian Australia revealed this week there is no cap on the amount of spousal flights senior ministers and other officeholders can claim under the rules, with regulations governing politicians expenses describing the entitlements as “relevantly unlimited in respect of total expenses claimable each year”.

But politicians have been widely criticised for the spending, including criticism that attending sporting events and even charging taxpayers to attend social occasions or take family members on interstate trips is badly out of step with community expectations.

Ley offered bipartisan support to reform the expenses regime, which the Turnbull government introduced in 2017 amid fury over Ley’s own travel.

“I can sit down with the prime minister anytime and go through measures that he would like to propose to implement to restore that public trust.”

Ley said Wells’ expenses were “scandalous” and questioned whether the minister should stand aside while the IPEA audit was underway.

The opposition leader also called for Wells to be investigated for any breaches to the Ministerial Code of Conduct.

“If he [Albanese] can’t stand there and tell the Australian people that this minister has not breached the code of conduct, then she should resign, stand aside. He should stand there and tell the Australian people clearly, No, she hasn’t breached my code,” she told Sky News.