Australia is at permanent risk of a second wave of coronavirus cases, the nation's chief medical officer has warned.

Brendan Murphy has told a Senate inquiry into the federal government's coronavirus response that authorities are keeping a close eye on Singapore, which initially tracked well but is now dealing with a surge in cases.

"They had a very similar approach to us but they've now had a second wave in their migrant worker population," he said on Thursday.

"We have to be very, very aware that whilst we've only had seven cases over the last 24 hours, we're in a wonderful position, but there is a permanent risk of further waves.

"This is a highly infectious virus and it can take off fairly quickly."

Professor Murphy said the most effective decisions to curb the spread of the virus were shutting the nation's borders and ensuring returning Australians were quarantined in hotels.

He says re-opening the borders will "absolutely" be the last measure to be eased, with no changes for at least three to four months.

"The international situation at the moment is such that any relaxation of border measures would be very risky," he said.

Prof Murphy says he was first made aware of the virus on January 1, when China gave an assurance it was animal to human transmission.

That changed about three weeks later.

"There was clear evidence coming from China that there was significant human to human transmission which was a game changer," he told the hearing.

"Once you've got human to human transmission you've got a significant risk."

Prof Murphy first briefed Health Minister Greg Hunt around January 19 and the national security committee of cabinet a few days later.

Acting Department of Health secretary Caroline Edwards said the government was working with Apple and Google on a tracing app to help with virus case tracking.

Privacy issues are being dealt with before the app is launched, she added.

From next week the inquiry will hold hearings twice a week, bringing back senior bureaucrats such as Prof Murphy for updates.

Treasury boss Steven Kennedy will appear on Tuesday.

It comes as the Auditor-General has fired a warning shot at the government over its rapid spending on virus measures.

"It is imperative that risk assessments are sufficiently hard nosed and candid, and do not present government and other entities with an over optimistic view of what may happen," the audit insights paper says.

It also says advertising guidelines should be followed and an active oversight of the budget maintained.

Labor leader Anthony Albanese says parliament should return to its usual sitting calendar so government decisions are scrutinised.

Federal parliament is set to return for a week in May.