NSW Police chief Mick Fuller has denied he has a “personal relationship” with Scott Morrison and now claims he has never taken in his bins after a storm of controversy over a phone call to discuss a police probe into the government.

The Prime Minister and the police commissioner were once neighbours and both men have previously told 2GB radio’s Ben Fordham that Mr Morrison sometimes took the police chief’s bins in.

But the NSW police commissioner now says that was “a joke”  and never happened.

“Of course he has never brought my bins in. I never had his number in my phone so from my perspective, it is right for people to judge that – but I didn’t have his contact and I think that speaks volumes,” he said.

“I have never been to his house. I have never been to The Lodge, I have never had a personal invitation from him to join his family or friends. Our relationship is a professional one.”

The Prime Minister has previously told 2GB listeners he did take the bins in.

“That’s what good neighbours do. That’s what they do. Mick is a great bloke and that’s the Shire way,” he said.

The police chief gave the Prime Minister an assurance that he would move the matter 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 area great diverter of my time,” he said.

“There is a whole range of reasons why I want the matter finished quickly but professionally and many of those are selfish.”

Scott Morrison has refused to stand Angus Taylor down. Photo: Getty

On the basis of the phone call, Mr Morrison said he did not plan to ask Energy Minister Angus Taylor to stand aside.

“At this stage the allegation itself is around a complex piece of criminal law,” Mr Fuller said.

“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?

“But again, I feel as though it was in the public’s interest that I acted on what was a well-constructed letter from the Shadow Attorney-General and, from New South Wales police’s perspective, I need to make sure we act openly and ethically with all members of our community.”.

“The Prime Minister 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.”

Earlier, former prime minister Malcolm Turnbull warned the government needed to be very careful not to raise concerns that political influence was being brought to bear on the investigation.

“It is always critically important in any police inquiry, particularly something that involves a politician, that the police are and are seen to be acting entirely free of political influence,” Mr Turnbull said.

“Now, I’m sure the call the Prime Minister made to the NSW Police Commissioner was innocuous but it would have been much better had it not been made. Because 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.”

“It is a call – being blunt about it – it is a call I would not have made.”