Last week, an average of 26,100 tests were done each day, well down on the week before, when an average of 30,600 tests were done each day. The week of May 11-17 remains the biggest testing week so far.

Brendan Murphy has nominated 40,000 to 50,000 tests a day as a number to aim for, but so far Australia hasn't achieved it.

Deputy Chief Health Officer Paul Kelly said testing rates had been high in mid-May when the states had a testing blitz.

In the 24 hours to Wednesday, 35,000 tests had been done - "not quite that 40-50,000 but it is a lot".

He also pointed to the very low rate of positive tests. Last week, just 0.6 per cent of tests, or about one in 200, were positive.

"We are continuing to see a very low positivity rate amongst those tests which demonstrates that we're testing enough," he said.

"You can only test what you have in front of you so, again, it is a call to people who have symptoms to come - any concerns at all to come and be tested. You will be tested."

A recent review of the more than 100 respiratory clinics set up for the coronavirus crisis showed that more than 95 per cent of people coming to those clinics are being tested, he said.

Australia averaged 102 tests per 100,000 people each day last week, down from 120 the week before.

The slump was especially pronounced in Canberra, where an average of 57 tests were done per 100,000 population each day last week, compared with 77 the week before. That puts Canberra back near the testing rate at the end of April. Only the Northern Territory and Queensland have lower testing than the ACT.

Testing also fell substantially in Victoria, which recorded an average of 177 tests per 100,000 population last week, well down on the 240 the week before. Victoria still has the highest testing in the country by far, well above NSW, at 98.

Queensland health authorities turned their focus on the small and isolated town of Blackwater, where a 30-year-old miner died on Tuesday after being sick for three weeks with what has now been diagnosed as coronavirus. No source for his infection has been announced but it was reported that a Rockhampton nurse with coronavirus had visited Blackwater.

The victim was by far the youngest Australian to die, Professor Kelly said.

Previously, the youngest death was a 42 year old male Filipino cruise ship crew member who died in Perth. Two people in their 50s have died. Otherwise, 99 of Australia's 103 deaths have been in people older than 60, and well over 80 per cent of deaths among people over 70.

Professor Kelly said the Blackwater death was a concern, indicating community transmission, and a "very strong reminder to all of us at this point that if anyone has any symptoms that are of a respiratory virus, a cold - it might feel like a cold, it could be COVID and we really want to get that test done".

There were fewer than 500 active cases, with 30 people in hospital, six in intensive care and three on ventilators on Tuesday, he said.

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On Friday, May 15, restaurants reopened for up to 10 people at a time in a number of states. Since May 17, 15 or fewer new cases have been recorded each day.

In NSW, where pubs and restaurants will open to 50 people at a time from Monday, authorities were trying to track the source of two cases among school children in the area near Bondi where there was an outbreak in March. A 10-year-old attended school for a day while infectious, and a 12-year-old attended a separate school for two days while infectious.