The Prime Minister has refused to apologise in the House of Representatives amid Labor accusations he misled the Parliament during a heated debate about Energy Minister Angus Taylor.

Key points: Labor wants Scott Morrison to front the Parliament amid accusations he misled the House of Representatives

Labor wants Scott Morrison to front the Parliament amid accusations he misled the House of Representatives The Prime Minister late on Wednesday corrected comments he made about Julia Gillard

The Prime Minister late on Wednesday corrected comments he made about Julia Gillard He made the comments while defending Angus Taylor, who is under pressure to step down from the frontbench

Late on Wednesday, Scott Morrison sent a letter to the Speaker to amend incorrect comments he made while defending a call he made to the New South Wales Police Commissioner.

The Prime Minister has faced broad political condemnation for calling Commissioner Mick Fuller about an ongoing investigation involving Mr Taylor and his office.

On Thursday, Labor leader Anthony Albanese repeatedly demanded Mr Morrison front the Parliament and publicly correct the record.

But the Prime Minister refused to do that when he broke his public silence on the matter during Question Time.

He said he opted for a letter, rather than making public comments, to correct the record because he was travelling to Sydney for a family event on Wednesday evening.

"That letter, which I authorised was provided to the House, it was tabled here by the Attorney-General to ensure that the House was immediately informed of the necessary correction that had to be made," he said.

"Now, Mr Speaker, that was followed up with a further letter to the clerk and as you advised the House last night, these are the appropriate forms of the House to correct the record."

Mr Morrison, while defending his decision to not stand down Mr Taylor during the police investigation, said then-prime minister Julia Gillard did not stand down during an investigation into a union slush fund from her previous career as a lawyer.

He told the Parliament a Victorian detective had said "the prime minister of Australia, Julia Gillard, is under investigation by police" but hours later had to clarify the comments were made by Sydney radio host Ben Fordham.

Scott Morrison had to correct a statement he made during a heated Question Time focused on Angus Taylor. ( ABC News: Toby Hunt )

"The Prime Minister should this morning at 9:30 come into the Parliament, correct the record in person, and apologise for misleading Parliament yesterday, when instead of the quote that he used allegedly from a Victorian detective, it was actually from a 2GB presenter," Mr Albanese said on Thursday morning.

"[It was] an extraordinary error in a pre-prepared answer, word for word, extensive quotes used to attack former prime minister Julia Gillard.

"It just shows yet again the lack of judgement that's been on display for all to see from this Prime Minister when placed under pressure."

Mr Morrison refused Labor's demand and was not present in the House of Representatives when Thursday's proceedings started at 9:30am.

Mr Albanese then sought to use parliamentary tactics to demand the Prime Minister front the chamber to correct his statements in person and apologise — a move that failed.

Angus Taylor was the focus of Labor's attention in Question Time on Wednesday. ( ABC News: Toby Hunt )

The Prime Minister was not present when his letter correcting the record was tabled in Parliament on Wednesday. Instead, Attorney-General Christian Porter delivered it.

While Mr Morrison corrected the record, he did not apologise for the error.

Mr Taylor and his office are under investigation by NSW Police over allegations a forged document was used in a political attack on the Sydney City Council and Lord Mayor Clover Moore.

Mr Taylor has repeatedly said neither he nor his office altered the letter used in an attack.

Speaking in Question Time on Thursday, he accused the Opposition of a "pathetic, outrageous accusation".

"Those opposite are all smear and no idea," Mr Taylor said.

Clover Moore was the target of accusations made by Angus Taylor. ( AAP: Dan Himbrechts )

Mr Morrison is also facing demands from Labor and the crossbench to release the transcript or notes from his call with Commissioner Fuller — a call both men insist was appropriate.

Crossbench MP Rebekha Sharkie said the saga had brought into question the integrity of the Parliament, and the respect members were showing for the House of Representatives.

"I think if the Prime Minister releases his transcript, that will certainly shed some light on the conversation," Ms Sharkie told RN Breakfast.

"And I think it would, if the conversation is as the Prime Minister said, which I'm sure it is, would then provide that clarity and that confidence needed within the Parliament."

Sydney's Lord Mayor said she shared concerns about the appropriateness of the phone call between Mr Morrison and Commissioner Fuller.

"A lot of concern has been expressed about that phone call the Prime Minister made to the Police Commissioner, and I share those concerns," Cr Moore said.

"I think it's important we know where the forged document came from, and I think that the minister should respond and give us that information."

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