Australia and New Zealand on Tuesday brushed aside calls for an easing of tough restrictions on travel and public gatherings despite their success in curbing the spread of COVID-19.

The number of new coronavirus cases in the neighbouring nations has fallen dramatically in the last two weeks, raising hopes that difficult social distancing measures may be relaxed.

But Australian Prime Minister Scott Morrison said the country was still "many weeks away" from lifting any restrictions.

"Patience has got to be our virtue here," he said, noting that countries like Singapore and South Korea had initial success against COVID-19 but saw a surge in new cases after travel and other restrictions were eased.

Australia registered just 63 new infections on Sunday and Monday, bringing the total number of cases to 6,366 for a population of 25 million.

It was the lowest two-day increase in a month.

New Zealand, a nation of five million, saw just eight new cases on Tuesday for a total of 1,072, its lowest daily increase in more than three weeks.

"We've been relatively successful -- I don't want to squander that success or the sacrifices New Zealanders have made," New Zealand Prime Minister Jacinda Ardern responded Tuesday when asked when the lockdown will be eased.

"Our goal has to be go early and go hard, so that we get into a position where we can ease up restrictions with confidence," she said, adding that no action would be taken for at least another week.

Both countries have closed their borders to foreigners and imposed 14-day quarantines on returning residents.

New Zealand has enforced a strict stay-at-home lockdown while Australia imposed tight restrictions on movement, gatherings and public activities.

"Australians are doing magnificently, we've seen real progress," Health Minister Greg Hunt said Tuesday, linking the slowdown in new cases to people honouring lockdown rules.

"The rest of the world would, overwhelmingly in a heartbeat, swap positions with Australia."

But the clampdowns have caused significant economic damage, with Australian officials Tuesday predicting unemployment will double to 10 percent despite a massive government spending spree to counter the impact of the pandemic.