Scott Morrison has rebuffed an invitation by Labor to release any officials’ notes of his conversation with the New South Wales police commissioner Mick Fuller, and insisted there was nothing inappropriate about approaching the police chief while he was investigating the conduct of one of his ministers, Angus Taylor.

Morrison mocked Labor for pursuing the propriety of the call in question time on Wednesday, declaring no objections were raised by the opposition on Tuesday when he flagged his plan to make contact with Fuller. The prime minister also accused Labor of double standards, declaring both Julia Gillard and Bill Shorten faced police probes, and did not vacate their posts.

But Morrison ran into trouble later on Wednesday when it emerged he had misled the House by incorrectly attributing a comment about the historical police investigation into Gillard to the detective handling her matter, when the comment had been made by Sydney talkback radio host Ben Fordham.

Morrison, who had left Canberra for the evening, corrected the record by writing to the Speaker, Tony Smith, acknowledging the botched attribution. Labor is demanding that the prime minister correct his mistake in person on Thursday morning. The government moved to shut down the opposition’s vociferous objections in parliament on Wednesday night, gagging motion after motion.

The Taylor controversy dominated federal parliament on Wednesday. The former prime minister, Malcolm Turnbull, ratcheted up political pressure earlier in the day, declaring he would not have phoned the New South Wales police commissioner to check the status of an investigation into the origins of an altered document.

Turnbull raised the political stakes by telling Sky News he was certain the conversation his successor had with Fuller about the Taylor investigation was “innocuous, but it would have been much better if it had not been made, because it is really, it is vitally important that that inquiry that is being conducted by the NSW police – like every inquiry they undertake – is seen to be conducted entirely free of political influence. Being blunt about it – it is a call I would not have made.”

As well as attempting to fend off Labor’s sustained attack about the propriety of the call to Fuller in question time, Morrison also shrugged off the pointed criticism from Turnbull. “Only those in possession of all of the facts ... can make any real judgment about the call I made,” Morrison said.

The Labor leader Anthony Albanese asked Morrison whether he had sought advice from officials before speaking to Fuller, and whether note takers had been present. Morrison said the “normal arrangements applied for those calls, and the normal processes apply for accessing that information in relation to those matters”.

As Labor doubled down, Morrison defaulted to mockery, asking whether Albanese thought he he was going to call the parking infringements officer at the Sutherland police station, the water police or the dog squad, or perhaps the commander of the police band?

Albanese asked why Morrison thought the normal rules of accountability did not apply to him. The prime minister said he thought that was more of a “smear” than a question, and he accused the Labor leader of “sulking”.

NSW police confirmed that just before question time on Tuesday they had launched an investigation into the origins of an altered city council document Taylor used to attack the Sydney lord mayor, Clover Moore. The document contained incorrect information about council travel. Taylor has apologised to the lord mayor.

With Labor insisting that Taylor should step aside for the duration of the police investigation, Morrison spoke after question time to Fuller and then made a brief statement in the chamber saying there was no need to take action against Taylor at this time.

He said Fuller had conveyed to him that the matters under investigation were “based only on the allegations referred by the shadow attorney general”.

In an interview in 2018 the NSW commissioner told Sydney’s 2GB radio station he used to be Morrison’s neighbour, and that the prime minister had collected his bins when he went away.

“He was the treasurer at the time,” Fuller said. “He did tell me recently that he’s the prime minister now, and that should be Josh Frydenberg’s job, but he won’t take my calls! He’s a neighbour of mine and I do wish him well – he’s a very good neighbour.”

While Morrison described Fuller in 2018 as a neighbour and a “good bloke” the police chief recanted the bin story on Wednesday, telling reporters: “From my perspective that was just a joke. Of course he has never brought my bins in”.

The NSW police commissioner said he did not have a personal relationship with Morrison and the conversation they had on Tuesday was uncontroversial. “The prime minister didn’t ask me any questions that were inappropriate”.

The police chief said he told the prime minister the investigation would be concluded “as quickly as possible”.

“To be honest with you, these types of investigations can consume an enormous amount of resources from New South Wales police and they are a great diverter of my time,” the commissioner said. “There is a whole range of reasons why I want the matter finished quickly but professionally and many of those are selfish”.

Ahead of question time, Albanese, declared it was “pretty unusual” for the prime minister to ring a police commissioner when an investigation was under way.

“For the prime minister to ring the police commissioner – not in the national interest, in his personal interest, to defend his government when he has an interest, clearly, in not having a minister step aside – I found it quite breathtaking when the prime minister came into the parliament yesterday and, instead of announcing that the minister would step aside, he did the opposite,” Albanese said.

He said Morrison’s job was to “act in the national interest when he talks to authorities, not in his own personal interest, and I found it pretty unprecedented, frankly, that he would suggest that there had been a discussion about details of an investigation that was only launched hours beforehand”.

Taylor has said repeatedly, including in parliament on Tuesday, that neither he, nor “any members of my staff, altered the [council] documents in question”. The minister says he will cooperate with the police investigation.

While signalling cooperation, Morrison told parliament on Tuesday it was likely that the police inquiry would come to naught because Labor made referrals to the police frequently, and “they’ve all ended up going absolutely nowhere at the end of the day”.

The shadow attorney general, Mark Dreyfus, wrote to the state police in late October requesting that Fuller investigate whether someone had “made a false document with the intention” of inducing journalists at the Daily Telegraph to accept it as genuine for the purpose of influencing the “Lord Mayor of Sydney, Clover Moore, and other City of Sydney Councillors in the exercise of their public duties”.

Dreyfus also asked police to examine whether an offence had been committed “on the basis that Mr Taylor or one or more individuals from Mr Taylor’s office” knew or believed an offence had been committed but failed to bring it to the attention of police.

He said an article in the Daily Telegraph on 30 September 2019 “regarding travel expenditure by the City of Sydney Council was based on a forged version of the Council’s annual report”.

“That forgery, which dramatically overstated the council’s annual travel costs, was allegedly provided to the newspaper by the office of the minister for energy and emissions reduction, Mr Angus Taylor.”

Taylor has flatly rejected the allegations and dismissed them as a “conspiracy theory”.