SYDNEY – Australia’s most populous state recorded no new COVID-19 infections for a third straight day on Sunday but extended raised social distancing and mask-wearing rules by a week as the authorities hunted for the source of a small outbreak.

After a Sydney couple tested positive to the coronavirus last week, ending a long run without community transmission, the authorities reinstated some social distancing measures until May 10, and a campaign to get more people tested, as they scrambled to determine the source of infection.

On Sunday, the authorities reported a third straight day without a new case, easing concerns about a wider outbreak in the city, but cited the mystery cause of infection as a reason for extending the measures.

“As the ‘missing link’ case hasn’t been identified we’re keen to prevent a super-spreading event,” said New South Wales state premier Gladys Berejiklian in a tweet.

“All safeguards/restrictions will be in place for an extra week, except for shoppers in retail who will no longer be required to wear a mask.”

That means the more than five million people living in and around Sydney must wear masks on public transport and in most public venues, while households are limited to 20 guests at any one time until May 17.

Australia has largely eliminated the virus, with 79 days in 2021 without a locally acquired case, according to the government, as a result of a strategy of closing international and domestic borders, as well as social distancing measures.

As the country awaits vaccine shipments and watches infection spikes in other countries, top lawmakers have said borders now appear likely to reopen in 2022, not 2021 as previously envisaged.

In an interview with News Corp newspapers published on Sunday, Prime Minister Scott Morrison said it was unlikely Australia would reopen its borders soon, although he did not offer a timeline.

“I don’t see an appetite for that at the moment,” he said, referring to border reopening.

“What we’re seeing at the moment is the appreciation of the people that the pandemic isn’t going anywhere. We have to be careful not to exchange that way of life for what everyone else has.”