The Australian state of Victoria recorded 466 new cases of COVID-19 and 12 deaths, including another man in his 30s.
The figures were released as the city of Melbourne remained in lockdown and under an overnight curfew.
Victoria Premier Daniel Andrews said that six of the deaths were connected to outbreaks at aged care facilities.
On Friday, when the state reported 450 new cases and 11 deaths, the chief health officer said the coronavirus infection rate in the hard-hit state had been relatively flat in the past week.
That was down from a record 725 infections reported a week earlier The deaths announced Saturday took the state's toll to 193 and the figure for COVID-19 deaths in Australia to 278.
Meanwhile, Queensland state's border with New South Wales has officially closed with road access blocked to everyone except essential workers and locals living along the interstate boundary. Police reported that nearly 150 people had been turned away in the early hours of the shutdown.
Queensland Chief Health Officer Jeannette Young declared New South Wales and the Australian Capital Territory, which contains the national capital Canberra, coronavirus hot spots on Saturday as the southern border closed for the second time since the coronavirus crisis began.
The Queensland government will review the border closure at the end of August. It has had few new COVID-19 cases in the past month.