Opposition Leader Peter Dutton says the prime minister should refer himself to the National Anti-Corruption Commission after evading questions about whether he made personal requests to former Qantas boss Alan Joyce for free flight upgrades.

Anthony Albanese fronted the media and returned fire after Nine Newspapers reported he had a direct line to Mr Joyce while in the transport portfolio, which he used to request upgrades to business class through the Qantas Chairman's Lounge program.

He dismissed that claim by columnist Joe Aston as made by a "person who is trying to sell a book", repeating that all free flight upgrades he had received had been properly declared.

Mr Albanese said the only discussions he could recall with Mr Joyce at the time were "not through calls", and related to the first A380 flight from Australia to Dubai.

"There is no accusations being made with any specifics at all about any of this. None," he said.

Dutton calls for self-referral for corruption probe

At a press conference on Tuesday afternoon, Mr Dutton said there were "lots of questions about [Mr Albanese's] credibility and integrity" in relation to the federal government's controversial decision to block a Qatar Airways application to expand its services in Australia.

The prime minister has denied Qantas lobbed him to reject that application, and the government has pointed to a track record it said showed the Albanese government had not been soft on Qantas.

Mr Dutton said Mr Albanese should "take the initiative to refer this matter to the integrity commission".

"If Prime Minister Anthony Albanese had not decided to support his mate Alan Joyce, I think we would find ourselves in a position where we would have lower airfares today … It is another example of the prime minister putting himself before other Australians," he said.

The opposition leader said Mr Albanese's justifications were not "coherent" and suggested he breached the ministerial code of conduct that applied to him as a minister in the Gillard government.

"He picked the phone up to Alan Joyce to request an upgrade of airfares, which is something I do not think you can provide an explanation to. I'm not aware of any transport minister before that having done that," he said.

"Every time he gets before the cameras he gets angry and is not good under pressure, which is never a good trait in a minister … We will see if he lives up to his own standards."

PM says Dutton 'nasty' and declarations appropriate

The prime minister repeated that he had declared all his flights, but said there were other politicians who had received more upgrades than him, or not fully declared their Qantas perks.

Mr Albanese added a "nasty" Opposition Leader Peter Dutton was obsessed with attacking him and his family, who have also benefited from the Chairman's Lounge program.

The Coalition is considering attempting to establish an inquiry and summonsing Mr Joyce to face questions over whether he had taken calls from Mr Albanese about flight upgrades.

The ministerial code that covered part of Mr Albanese's time in the transport portfolio required that ministers not seek or encourage "any form of gift in their personal capacity".

Mr Albanese took a swipe at Mr Dutton over two private flights he took courtesy of Gina Rinehart's Hancock Prospecting, both of which were declared.

"I didn't have to declare any flights on private jets owned by billionaires like Gina Rinehart because I haven't engaged in it — as simple as that," Mr Albanese said.

"And it's up to Mr Dutton to explain how those flights were organised to private parties."

Mr Dutton declared a third flight, funded by billionaire Tom Roberts's Warburton Group, to attend Ms Rinehart's National Mining Day gala at Roy Hill in Perth.

Mr Dutton said he had been "very transparent" about the flights.

"I have declared all of that, which is why [Prime] Minister Albanese knows about it," he said, adding he had not personally called Ms Rinehart to ask for travel to be arranged.

Mr Albanese declared a helicopter flight from Avalon to Portsea in January last year to attend a private lunch, courtesy of transport billionaire Lindsay Fox.