The ex-police chief's recollection of a phone call at 1.17 pm on March 27 was detailed in a fresh sworn statement tendered to the inquiry on Friday.

It was one of a raft of documents called for by the inquiry in a final attempt to nail down who made the decision that ultimately led to Victoria's second coronavirus wave.

Mr Ashton wrote that he and Mr Eccles spoke for 136 seconds following a meeting of the national cabinet.

"At least part of this conversation involved Mr Eccles informing me regarding the potential use of the ADF to guard returned travellers during the transfer from their flights and the use of private security to guard them at the hotels," he wrote.

"But my belief as to what he told me in this regard is based only on the inference which I draw from the contents of the text message which I sent to AFP Commr Reece Kershaw".

This text to Mr Ashton's AFP counterpart was sent just minutes after the call with Mr Eccles, saying he had been advised private security would be used.

Mr Eccles maintained he could not recall the content of the conversation with Mr Ashton and was adamant he had "no knowledge" of any decision to use police, the ADF, the AFP or private security.

"I also did not have the expertise to make such decisions," he wrote.

The top bureaucrat resigned from his position after his phone records revealed the time of his call, but denied all responsibility.

A summary of the March 27 national cabinet meeting by Department of Health and Human Services bureaucrat Nicole Lynch was mentioned throughout the new tranche of documents, particularly the line: "Enforcement by S and T governments keen for police not to babysit but called in as need (eg use private security)".

Premier Daniel Andrews said in his sworn statement he did not take this to be a decision about private security and therefore did not pass it on.

"Decisions of that kind are of an operational nature in which I do not play a role," he wrote.

Text messages between Mr Andrews and his chief of staff Lissie Ratcliff on the evening of March 27 show him telling her to expect updates on logistics of hotel quarantine, such as rooms available, transportation and guidelines for travellers.

Professor Brett Sutton provided a second sworn statement to the inquiry, after he at first gave evidence that he didn't remember an email exchange with health bureaucrat Euan Wallace about the quarantine program.

In his new statement, Prof Sutton said he did recall emailing Professor Wallace on April 13, but he did not remember this when giving sworn evidence on September 16.

"I now also have some recollection of speaking to Prof Wallace on the matters raised in those emails but do not recall that we came to any resolution or conclusion," he said.

He maintained his public health team was not involved in the quarantine program and that they "did not have operational control" over parts of the public health response "for which they had a moral and perhaps legal responsibility".

Victoria's hotel quarantine program was established within 36 hours of a national cabinet meeting on March 27.

Outbreaks among security and hotel staff at Rydges and Stamford Plaza have been blamed for 99 per cent of Victoria's COVID-19 second wave.

The second wave resulted in more than 18,000 new infections and 750 deaths.

The hotel quarantine inquiry board is due to hand down its full report by December 21.

Australian Associated Press