Returned overseas travellers who refuse to be tested for the coronavirus on the tenth day of their hotel quarantine in New South Wales will now be required to stay longer.

NSW Health made the announcement on Saturday as the state reported six new cases of the virus, including five currently in hotel quarantine.

Travellers returning to NSW have been asked to undergo testing on the tenth day of their quarantine since May 15, and less than two per cent of people have refused so far.

From now on, anyone who does will be required to stay an extra 10 days.

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The new rule comes after it was revealed up to 30 per cent of returned international travellers in Victoria are refusing to be tested.

“We think that will be a very clear message to them that perhaps they better have the test,” NSW Health Minister Brad Hazzard said.

Of the 11,634 travellers who have been tested for COVID-19 on day 10 of their stay so far, 59 have been found to be positive.

“These cases are in addition to the 3314 returned travellers who have shown symptoms of COVID-19 and been tested in NSW quarantine hotels, before or after day 10,” NSW Health said.

“Since 29 March, 105 of those symptomatic returned travellers have been found positive.”

There is no requirement compelling travellers to take a test in Victoria, although they are given multiple opportunities throughout their stay, deputy chief health officer Annaliese Van Diemen said.

Those who refuse tests have been labelled “reckless” and “selfish” by both Labor and Liberal politicians.

“Frankly, I think it is recklessly indifferent of people in quarantine not to agree to have a test, because we’ve seen the number of people that are in quarantine testing positive is obviously a lot higher than the rest of the population,” Liberal MP Trent Zimmerman told ABC TV on Saturday.

“If they are not prepared to do that, they shouldn’t come back.”

But Dr Van Diemen said there was no evidence people leaving hotel quarantine were spreading the virus.

“The evidence remains that we’re not seeing cases in our community that have leaked out of hotel quarantine because they haven’t been tested. We’re just not seeing them,” she said.

The six new cases reported in New South Wales on Saturday bring the state’s total number of cases to 3174.

The remaining case involves a man in his 70s from Penrith, in western Sydney.

NSW Health said the case was under investigation and all close contacts had been contacted.

A total of 58 active coronavirus cases are now being treated by NSW Health, with none in intensive care.

More than 810,000 tests have been carried out across the state.