In an extraordinary attack, outgoing Liberal Concetta Fierravanti-Wells laid into the prime minister during a fiery late-night parliamentary speech on Tuesday.

The senator, who lost preselection for her NSW upper house seat at the weekend, claimed just hours after the pre-election federal budget was revealed that Mr Morrison was “not fit to be prime minister”.

“He is adept at running with the foxes and hunting with the hounds, lacking a moral compass and having no conscience,” she told the Senate.

“In my public life, I have met ruthless people. Morrison tops the list followed closely by (Immigration Minister Alex) Hawke. Morrison is not fit to be prime minister, and Hawke certainly is not fit to be a minister.”

However, Morrison said being criticised went with the territory.

“As prime minister, there are lots of people who will disagree with you, there are lots of people who will say all sorts of things about you,” he told Sydney radio 2GB on Wednesday.

“It comes with the job. You’ve got to have a thick skin and you’ve got to be able to focus on the things that matter most to Australians.”

But Opposition Leader Anthony Albanese said while the prime minister had been quick to point out the need for culture reviews within the Labor Party, he had not addressed issues within the Liberal Party.

“Those people who know Scott Morrison well attest to the flaws in his character,” he told ABC News on Wednesday.

“It’s extraordinary that a sitting serving senator who’s been a former minister, who has served alongside in the ministry with Scott Morrison, says he is unfit to be prime minister. Those comments do say a lot.”

Fierravanti-Wells also labelled Morrison an “autocrat”, adding that other members of the Liberal Party share a similar view.

“They have lost faith in the party, they want to leave. They don’t like Morrison and they don’t trust him,” she said.

Fierravanti-Wells was been relegated to an unwinnable spot on the Liberals’ NSW Senate ticket.

“I know Connie’s disappointed that on the weekend 500 members of the Liberal Party went to a preselection and they didn’t select Connie,” Mr Morrison said.

“I understand that and I understand that there are many disappointments in political life.

“When you are prime minister, people hold you responsible for many, many things and there are decisions taken over your life as prime minister that can lead to disagreements.”

In her Tuesday night speech, Fierravanti-Wells also accused the prime minister of making racist comments during his preselection battle for the NSW lower house seat of Cook in 2007.

“I’m advised that there are several statutory declarations to attest to racial comments made by Morrison at the time that ‘we can’t have a Lebanese person in (the federal seat of) Cook’,” she said under parliamentary privilege, referring to an alternative candidate who was also seeking Liberal preselection.

Morrison said her claim was “rubbish”.

Pressed on the issue, he said: “It’s not true”.