Health Minister Chris Hipkins says the country's latest case of Covid-19 visited an Auckland supermarket last night.

Hipkins said the man left his managed isolation last night to go to the Countdown supermarket on Victoria Street in central Auckland.

He said after CCTV footage was viewed and the man was interviewed, the current assessment of the risk to the public was low.

"The person wore a mask although indicated that was removed for short periods of time."

The Countdown remained closed today in order to be cleaned thoroughly.

Hipkins said all Covid-19 facilities were on standby and people needing a test would have no problems getting one.

Individuals within these facilities need to "play by the rules", he said.

"These are acts of selfishness and we intend to use the full weight of the law."

Yesterday, 2131 tests were completed.

Two new cases were confirmed yesterday, both are from the same family and had arrived from Afghanistan.

Hipkins yesterday said the levels of testing for Covid-19 were now not meeting the government's expectations with 1641 tests completed on Monday.

"We don't need to be testing at our peak level ... but we do want to maintain a good level of surveillance across the country," he said.

However he said he expected the level of surveillance testing could be ramped up to the recommended level of 4000 tests within days.