All members of the small group of Liberal cabinet ministers became unintended suspects after the texts were put to Scott Morrison during his National Press Club address on Tuesday, but only the identity of one half of the conversation was revealed and Ms Berejiklian later said she had no recollection of the exchange.

Foreign Minister Marise Payne and Energy Minister Angus Taylor are among the ministers denying involvement in the texts that Channel 10 claimed were sent during the Black Summer bushfires while Mr Morrison holidayed in Hawaii. Communications Minister Paul Fletcher and Home Affairs Minister Karen Andrews have also ruled out taking part, while Deputy Nationals leader David Littleproud has described the Liberal leaking as "games" and a "titillation of Canberra."

"Yeah. I don't think it's a great revelation that some people don't like one another down here in Canberra. That's been the nature of this place for some time. It's competitive," the Nationals MP told the ABC on Wednesday.

"It's a place where it's bringing together people from diverse backgrounds that wouldn't necessarily be friends outside of politics."

Mr Morrison brushed off the scandal and agreed with a statement put to him on radio Wednesday morning that the minister responsible for the texts was not currently sitting in his cabinet. "I have confidence" was his response when pressed on why he thought that.

"I'm not fussed," the Prime Minister said when asked if he had sought an investigation into their identity.

Deputy Prime Minister Barnaby Joyce told local reporters in his electorate of New England that the leaker should come forward and identify themselves or a journalist would do it for them.

"I would suggest that if you know anything about this don't wait to be outed, out yourself," he said.

"And give an explanation. Maybe it was a bad day in the office, I don't know. That's a better way to do it."

"The fact they don't necessarily get on, I don't think really matters. We've had great partnerships; Hawke and Keating, Howard and Costello. I don't think they were sitting every Friday night knocking over a couple of tinnies over together but they got the job done and respected one another."

Ms Andrews said the focus on the leak was a very disappointing outcome from Mr Morrison's speech about the future of manufacturing and the national recovery, which had been a positive message.

"He doesn't always agree with some of the things that I put to him, but I always get a fair hearing, and I don't expect that everything that I put up is going to be immediately accepted," she told 4BC. "So we shouldn't be reading anything into that. I've always found him very firm and very fair."

Senator Payne, the most senior woman in cabinet, said she had never used the language reportedly in the text exchange and questioned if the leak was genuine.

"I would add that I also reject the description of the Prime Minister in the purported messages," the Foreign Minister told reporters in a statement. "They do not match my long experience of working with him. He is the best person to lead this country now and into the future."

Labor leader Anthony Albanese says the alleged text messages during the devastating bushfire period are "extraordinary" and appear to be from people who know Mr Morrison the best.

"The statement from the former premier, the premier at the time, where she said this, 'Lives are at stake today and he's just obsessed with petty political point-scoring', I think is devastating," he told reporters.

"I think that alone is enough to disqualify him from being someone who secures a second decade in office. Australians deserve better than that.

"The cabinet minister, of course, and I don't know who the cabinet minister is, said also the mob have worked him out and think he's a fraud. Well, if people who are Liberal cabinet ministers think that, Australians will make their own judgement."

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