The political furore around Angus Taylor has escalated, with Prime Minister Scott Morrison having to defend his unconventional action of ringing NSW Police Commissioner Mick Fuller to inquire about the investigation into an alleged doctored document used by the energy minister.

Critics of Morrison’s call included former Prime Minister Malcolm Turnbull, who said while he was sure the call was “innocuous … it would have been much better had it not been made”.

“It is vitally important that that inquiry … is seen to be conducted entirely free of political influence,” he said. “Being blunt about it, it’s a call that I would not have made.”

After NSW police announced it was investigating the circumstances surrounding the document – containing highly inflated figures that Taylor used to try to discredit the City of Sydney over its travel expenses – Morrison said he would “take advice” from the police before assessing Taylor’s situation.

After ringing Fuller, he indicated Taylor would not be stood aside during the investigation.

On Wednesday, Morrison told parliament: “What I did yesterday is what I told the house I would do.”

“The purpose of my call was to fulfil my undertaking to the house and to discharge my responsibility under the statement of ministerial standards to inform myself of the nature, substance and instigation of the investigation under way.

"I do not intend to base serious assessments of my duties under the statement of ministerial standards on media reports or comments made by the Labor Party.”

Fuller, who knows Morrison personally, defended the prime minister’s action when questioned on Wednesday.

“The prime minister was trying to confirm or deny whether or not there was an investigation into one of his cabinet members,” the commissioner said.

Fuller said he had received a letter from the shadow attorney-general, Mark Dreyfus, about the Taylor matter. Given the positions of Dreyfus and Taylor, “it was appropriate that we look into the matter to see if there was any criminality and to see if there was potentially a person responsible for that.”

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Read more: Scott Morrison stands by energy minister Angus Taylor, who faces police probe

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Fuller said Morrison “didn’t ask me any questions that were inappropriate. He didn’t ask for anything that was inappropriate and I’m comfortable with the discussion that we had over a few minutes”.

The commissioner said “the allegation itself is around a complex piece of criminal law. We are unsure at this stage even if we have reached a benchmark of it being a criminal matter. Now that needs to be the first port of call. Is this a criminal matter or is it not?”

He added he wanted the matter wrapped up as quickly as possible.

Fuller also played down the closeness of his relationship with Morrison, saying the prime minister was his local member and he had met him a few times but “I have never had dinner at the Lodge”.

“I certainly don’t have a personal relationship with the prime minister.”

Fuller once told 2GB’s Ben Fordham that when Morrison was his neighbour, the then-treasurer used to bring in his rubbish bin. When asked about that on Wednesday, he said this was just a joke. “Of course, he has never brought my bins in.”

Morrison was also previously asked by Fordham about whether he’d brought Fuller’s bin in, and responded, “that’s what good neighbours do”.

In parliament, Morrison defended not requiring Taylor to stand aside during the investigation by pointing to instances where Labor figures had not stood aside.

When asked by the media whether it had been inappropriate for Morrison to ring Fuller, opposition leader Anthony Albanese said:

“I’ll tell you what Australians will be thinking today … They will think to themselves, ‘If one of my mates was under investigation, can I pick up the phone to the head of the police and ask for the details of that investigation on the day that it’s launched?’ I think not.”

Michelle Grattan does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.