Victoria has recorded its highest number of new coronavirus cases in three weeks as hundreds of school students in two states go into self-isolation.

The state reported 12 fresh COVID-19 cases on Monday – seven linked to one family.

The spike represents Victoria’s highest number of new cases since May 22.

Those family infections are part of a cluster sparked by an asymptomatic doctor who may have picked the virus up from a patient. It has grown to 11 infections.

A second person who attended the Black Lives Matter march in Melbourne in early June has also been confirmed with the virus. One protester was a confirmed positive case last week.

In Melbourne’s south-east, Pakenham Springs Primary School has been closed for at least 24 hours for deep cleaning and contact tracing after two of its students were confirmed among the new family cluster.

In the city’s north, a second school – St Dominic’s in Broadmeadows – has also been closed after two students tested positive.

Monday’s spike comes after Victoria reported nine coronavirus cases on Sunday. It also had a new outbreak linked to a patient at Monash Health – with a healthcare worker and a close contact of the patient bringing that early cluster to three.

Victoria’s Chief Health Officer Brett Sutton said a woman tested positive after attending the rally but argued it was very unlikely she would have been infected at the protest.

Professor Sutton said she had worn protective equipment and had mild symptoms, making it unlikely to have transmitted the virus.

“Because we’ve prompted everyone who’s attended the protest with any symptoms … to come forward for testing, this individual has been identified as a positive case,” he told reporters on Monday afternoon.

“It’s really in that first week that people overwhelmingly develop symptoms, so any cases really should be out there now,” he said.

In NSW, three virus cases were confirmed on Monday as health authorities continued to investigate how a teacher at Laguna Street Public School in southern Sydney became infected.

Two were returned travellers in hotel quarantine.

But the third infection, an Illawarra man in his early 20s, remains a mystery. NSW Health is investigating his case – which comes after the state had enjoyed a period without community transmission of the coronavirus.

All of Laguna Street Public School’s students have been deemed close contacts of the infected teacher. They are self-isolating and will learn from home until June 24.

There are also three cases in an emerging cluster at Melbourne’s Monash Health. Photo: Getty

Victoria further eases restrictions

Cafes, restaurants and pubs will be able to increase their capacity from 20 to 50 patrons from 11.59pm on Sunday, while cinemas and theatres will also open their doors next week.

Patrons will be able to order a drink without buying a meal, but they will need to be served at a table, rather than the bar.

Non-contact sport will return for all age groups from next Monday (June 22), as will skiing, with the season to start from that date.

The announcement to ease restrictions came as the state recorded nine new coronavirus cases on Sunday.

About 600,000 Victorians have been tested for the virus.

NSW supports continued hotel quarantine for travellers

NSW Premier Gladys Berejiklian has credited the hotel quarantine system for returned travellers with keeping the community safe during the COVID-19 crisis.

She said infection rates in returned travellers have been high, with up to 4 per cent testing positive to COVID-19.

“It’s way too soon to think about changing quarantine,” she said on Monday.

“That’s something we’ve done which I believe has kept the community safe and that should continue in the foreseeable future because the risk is there.”

Ms Berejiklian also said she was open to using hotel quarantine to get international students back into NSW universities, but insisted there would be no reduction in the 14-day period.

She reiterated her concerns about a potential second wave of infections and an increase in community transmission cases as restrictions are eased.

“The virus is scarily contagious; it’s deadly,” she said.

“Whilst we are doing really well, incredibly well, it won’t last if people relax and if people don’t stick to the rules.”

In the latest easing of COVID-19 restrictions in NSW, the 50-person limit on indoor venues will be scrapped from July 1.

Pubs and restaurants are among venues that will instead be guided by a “one person per four square metres” rule. The same change also applies to funeral attendees and venues.

Outdoor cultural and sporting venues with seating of up to 40,000 will be allowed to hold 25 per cent of their capacity from July 1.

Queensland records another day without new cases

In Queensland, 100 mourners will be allowed to attend funerals from Tuesday.

The move doubles the number of people allowed to attend.

State health minister Steven Miles said limiting numbers of mourners had been one of the hardest restrictions to implement.

“It’s an event that people don’t get to choose the timing of,” he said on Monday.

“We’ve received hundreds of heartbreaking stories from families, wanting to have more people to grieve their loved ones.”

Funeral organisers will have to keep a list of names and contact details of attendees for eight weeks, and provide it to authorities if any of them are diagnosed with coronavirus.

Queensland again has no new confirmed cases overnight, with the number of active cases remaining at five and the total at 1065.

Despite a streak of low cases, Premier Annastacia Palaszczuk on Monday said the government would not considering opening borders before the end of June.

Nationwide, there are 7320 confirmed cases of the coronavirus, 102 people have died and 6838 people have recovered.

-with AAP