The Australian Tax Office is close to striking a deal with the Federal Court to fast-track large corporate tax cases that have dragged on for years.

Tax Commissioner Chris Jordan said the ATO had "hardened its approach" to corporate tax avoidance and was refusing to be "stooged and gamed" by companies that do not deal in good faith.

He said the court was receptive to making changes that would speed up significant cases - some worth hundreds of millions of dollars in unpaid taxes to the public purse - through the system.

The ATO believes the public is being short-changed by about $2 billion a year by corporate Australia.

"We are in discussions - it started last year - with the Federal Court to see how we can get some of these more strategically important cases up into their list in a quicker way," Mr Jordan told the Senate's corporate tax avoidance inquiry on Thursday.

"They are very co-operative and interested in how we can appropriately identify and work with them to get things up quicker."

The aim would be to prosecute "strategically important" cases to establish principles to then expedite a backlog of similar cases and potentially reduce the need for expensive courtroom showdowns.

Mr Jordan used the example of the ATO's case against Chevron, the owner of Australia's biggest ever resources project, the Gorgon liquefied natural gas plant off the coast of Western Australia.

The Federal Court last year ordered the company to pay $300 million in back taxes. The case had cost the ATO $10 million in legal fees and took more than 11 years from start to finish.

Mr Jordan fronted the inquiry in the same week his deputy Mark Konza chaired a meeting of 35 countries wanting to respond to the Panama Papers leak.

According to the ATO's knowledge of the leak, there are bikies and drug dealers among the Australian clients of Panamanian-based law firm Mossack Fonseca, which created tax-shielding shell companies on an industrial scale.

Mr Jordan said 80 of the 800 Australians so far implicated are on the Australian Crime Commission's list of "serious and organised crime holdings". They range from "bikies to promoters of tax schemes", according to ATO Deputy Commissioner Michael Cranston.

Mr Cranston confirmed that the Cayman Islands was a tax haven, but said it was generally considered a "US route" or destination for money from the United States.

Last year Labor senator Sam Dastyari called on Prime Minister Malcolm Turnbull to sell out of his $1 million investments in the Caymans through two Wall Street hedge funds that use Grand Cayman as their business address.

On Thursday, Fairfax Media revealed that 40 prominent Australians had written an open letter in response to the Panama Papers calling on Mr Turnbull to act to prevent wealthy Australians hiding money offshore and out of reach of the ATO.

Mr Turnbull responded by saying Australia was "leading the charge" since the Panama leak.

"We have a very strong taxation regime and we believe that everybody must pay their tax, must pay their fair share of tax in accordance with Australian law; no exceptions, no ifs or buts," he said.

The government is expected to unveil new measures in the budget to net more tax from multinational companies operating in Australia.

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