Outgoing Liberal senator Concetta Fierravanti-Wells last week made the accusations under parliamentary privilege, claiming Mr Morrison told party members they couldn't have a Lebanese person as a candidate for the NSW seat of Cook.

The prime minister was again forced to deny the allegations during a press conference on Sunday.

"These are quite malicious and bitter slurs, which are deeply offensive, and I reject them absolutely," he told reporters in Tasmania while making a funding announcement for the Marinus Link electricity interconnector project.

Such questioning is becoming a daily occurrence and overshadowing his attempts to sell last week's federal budget.

"I don't think anyone believes the prime minister, frankly," Dr Chalmers told Sky News' Sunday Agenda program.

"I don't think people believe the prime minister more broadly."

He says there is a pattern where people who know Mr Morrison the best, and work with him the closest, have the lowest opinion of him and are least likely to trust him.

But Treasurer Josh Frydenberg said the prime minister had categorically denied such claims.

Asked on ABC's Insiders program whether anyone had come to him with concerns about Mr Morrison's language or behaviour, Mr Frydenberg said: "No."

Social Services Minister Anne Ruston said it was a "political hit-job".

"It is disappointing to see such a calculated, political hit-job on the prime minister on the eve of the election by his enemies," she told Sky News.

"I don't think there has been any prime minister who has done more for the multicultural communities of Australia, including the Lebanese community."

Australian Associated Press