Nev Power owns a private Embraer EMB-505 business jet, in which he has piloted government ministers, offering them lifts to Perth in April and May.

The government is paying him an allowance for his use of the plane for commission business. The allowance assumes a weekly return trip to Perth, costed at $6000, although Mr Power told the Senate inquiry he had only made the trip four times as of the beginning of June.

Labor's Kristina Keneally has questioned Mr Power about the more than 20 flights his jet had made since his appointment at the end of March. He responded that the plane was used for charters when he was not using it. He later clarified that flights made to Merimbula, Mount Isa and Adelaide on April 23 and 27 had in fact been his.

Mr Power initially told the inquiry he went to Merimbula to visit a close friend in Bermagui, but corrected the record a few hours later, saying he had been mistaken and his visit to Merimbula had in fact been a business trip.

He had an exemption from coronavirus border closures for the Mount Isa trip as an essential agricultural worker, he told the inquiry. Responding to questions on his behalf later, a spokesperson for the National COVID-19 Coordination Commission in the Department of Prime Minister and Cabinet said he hadn't needed exemptions for the other locations. That was because he "travelled through Merimbula and Adelaide for refuelling which did not require exemptions", the spokesperson said, later clarifying that "the stop in Merimbula was to refuel and drop something off. The Adelaide stop was to refuel".

Now, Mr Power's plane has been removed from the public FlightTracker register. Asked why, a commission spokesman said the charter company had blocked tracking to ensure the security and privacy of private clients.

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Mr Power's use of his plane was "a private matter within those arrangements", the spokesman said, referring to his allowance to cover travel costs.

Mr Power would disclose details of his commission-related flights if requested by the Senate inquiry, the spokesman said.

The commission was set up by Prime Minister Scott Morrison at the end of March in the heat of the coronavirus crisis to ensure supply chains were secure and to provide a link from government to business so "problems" could be quickly solved.

It has run into controversy already over its promotion of the gas industry, with some of the commissioners and advisers working in the industry, and a report from "special adviser" Andrew Liveris calling for government support for the industry and major investment in gas supply lines, including a cross-continental line.

Data provided to the inquiry shows the commission is top-heavy in senior staff, with a full third of its staff in the senior executive service as of May 26. It has 12 SES staff, 16 executive-level staff and eight APS-level staff.

Three other staff, one at SES level and one at EL2 level, are full-time on coronavirus communications.

The commission is costing $3 million for its six-month life, with a substantial portion going towards pay and consultants. Mr Power gets $294,000 for his six months from March 23 to September 22. Deputy chairman David Thodey requested no pay, but will be reimbursed for any travel and other costs. Greg Combet and Jane Halton are getting $119,000 each, Paul Little $108,000 and Catherine Tanna $54,000.

Mr Liveris is not receiving pay but will have costs reimbursed, the commission said.