The issue has blown up for Abbott, who was elected to office last month vowing to lead a government that would "live within its means", while in Indonesia for the APEC summit.
Last week he voluntarily repaid about USD 1,600 in travel expenses claimed for attending the weddings of two former colleagues in 2006.
He did so following uproar after two senior members of his coalition were heavily criticised after being exposed for billing taxpayers thousands of dollars to go to the wedding of a radio host.
Today, Australian media also revealed Abbott, who has a macho reputation, charged taxpayers almost 1,300 dollars in travel and accommodation costs to compete in a 2011 ironman event, in which you run, ride a bike and swim.
He also routinely claimed a travel allowance and flights to take part in the annual 1,000 kilometre Pollie Pedal charity cycling trip through regional Australia that lasts several days, it was reported.
"I believe that all of my claims have been within entitlement," he told reporters on the APEC sidelines, adding that "the great thing about Pollie Pedal is it takes me to towns, communities, sometimes hamlets that rarely see a politician".
But with the furore growing, he admitted: "People should be careful and cautious when they claim entitlement. If there is any doubt they should resolve the doubt in favour of the taxpayer."
In an editorial, the Sydney Morning Herald said Abbott's government needed to lead by example having come to office promising no excuses, "but now they are coming thick and fast".
Bill Shorten, who is campaigning to be Labor leader following Kevin Rudd's defeat to Abbott in October elections, said the system needed to be tightened.
"I don't think most MPs -- the vast, vast, vast majority -- are out to do anything wrong," he told ABC radio.
"But if there is this confusion and there is this uncertainty, then it does need to be cleaned up for the public confidence in the system, full stop -- it does need to be sorted.
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