Reports in the Nine newspapers say Mr Dutton had engaged in $30 million worth of property transactions across three decades, while a story on News.com.au shows he had bought shares before the then-Labor government bailed out financial institutions.
But the opposition leader said he was happy for the details of his past to be scrutinised as he was vying to become prime minister.
"I've declared all the detail that's required to be declared," he told reporters in Sydney on Wednesday.
"The prime minister's office is shopping around dirt sheets at the moment - transactions that go back to when I was 20 years of age.
"If the prime minister has some claim to make, don't get his lackeys to push it out there, get up and make the claim yourself."
Many "astute investors" were buying bank shares at that time, Mr Dutton said, and he had been purchasing shares since he was 18 years old.
"I've been honest about my story ... I've been proud of what my family and I have been able to achieve," he said.
"I've conducted myself with integrity at all times.
"It reflects poorly on the prime minister and the desperation that he's in at the moment."
Prime Minister Anthony Albanese would not comment on the issue, but his cabinet minister Murray Watt said there was a double standard at play because Mr Dutton had committed to scrapping Labor's plan to build thousands of houses.
"It's fine for Peter Dutton to amass a large property portfolio for himself, but he wants to deny working Australians and essential workers in Australia the opportunity to have a home of their own," Senator Watt told reporters in Canberra.
"It's not the only thing he wants to cut."
The coalition has threatened to slash the public service if it forms government, but the details of its plan are unclear, prompting the workplace relations minister to challenge his opposition rival Michaelia Cash to a National Press Club debate.
"No more weasel words, no more delay, front up and tell the Australian people what you intend to do to their jobs and wages after the election," Senator Watt said.
Senator Watt warned the coalition's proposal would send Australia backwards as taxpayers would end up paying more to outsource government work to consultants.Â
Almost $21 billion was spent on an external workforce of 53,000 employees during the final year of Scott Morrison's coalition government.
Senator Watt also said the coalition needed to answer industrial relations questions about Mr Dutton's commitment to repeal Australians' right to disconnect from work communications outside of hours, and whether it would support a government bid to stop big companies from cutting penalty rates.
On Monday, the opposition revealed it would cut some of the 36,000 additional public servants hired by Labor to address excessive spending and fund its pledge to match the federal government's $8.5 billion Medicare boost.
But Mr Albanese maintains the opposition leader will undermine Medicare.
"Only Labor governments that will prioritise health care, prioritise education, dealing with cost-of-living pressures, whilst Peter Dutton continues to be negative and wage an ideological contest - which is what he would do when it comes to health care," he told reporters in Melbourne.
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