Prime Minister Malcolm Turnbull has defended his offshore investments after the Opposition claimed he was using a tax haven to avoid playing by the same rules as the rest of Australia.

Labor frontbencher Sam Dastyari used parliamentary privilege to question why Turnbull had invested in companies that have offices in the Cayman Islands, a well-known Caribbean tax haven where the corporate tax rate is zero.

“There is one reason people invest in the Cayman Islands – so they don’t have to play by the same rules as the rest of us,” Senator Dastyari said in a short speech to the Senate.

“This isn’t fair and it’s not right.”

Senator Dastyari said the investments were “all legal and disclosed” but asked: “Is any of it appropriate?”

Then he claimed Turnbull’s personal wealth could make it harder to crack down on big companies evading tax.

“Every time the Liberal Party votes against tax transparency, remember there is a house in the Cayman Islands – a house where Malcolm’s money resides,” he said.

The attack continued in Question Time and the Prime Minister, who is one of the richest members of Parliament, accused Labor of running a new campaign on the “politics of envy”.

He said to avoid conflicts of interest, almost all of his financial investments are in overseas managed funds, which means he has no say what companies they invest in.

“The consequence of that arrangement is that all of that income that accrues to my share of the investment is brought to account fully – and tax is paid on it – fully in Australia,” Turnbull told Parliament.

“It actually increases the tax that is paid in Australia.”

He said all of his investments were approved under the Ministerial Code of Conduct when he became a minister and he claimed Labor had no understanding of how managed funds worked.

“No Australian tax is avoided,” he said.

“I think if honorable members opposite look at their superannuation funds, they might find that many of them are invested in international managed funds, which are domiciled in the Cayman Islands.”

Turnbull’s investments and those of his wife are listed in the declaration of member’s interests.

The Prime Minister has dismissed similar attacks in the past, though this is the first time Labor has so publicly raised his personal wealth since the Liberal leadership spill.