The minister thanked Australians for staying home, saying: “Your actions are making a difference and saving lives.”
As of 6am on Tuesday morning, there were 4359 confirmed COVID-19 cases and 19 deaths in the country.
There were 50 patients in intensive care, including 20 on ventilators.
Mr Hunt said the fact that more than 230,000 tests had been conducted meant Australia’s numbers were reflective of the actual level of infection in the community.
But, he said, while progress had been made on “flattening the curve”, there was more to do.
Deputy chief medical officer Nick Coatsworth, an infectious disease expert from ANU, said Australians must not “take the foot off the pedal”.
“The restrictions that the minister and the Prime Minister have introduced on gatherings are absolutely essential to prevent the virus from making its only move, which is from one person to another,” Dr Coatsworth said.
“So, I would urge all Australians, follow those instructions to a T. Look towards your state governments for exactly what they are telling you to do.”