Melbourne, Jun 15 (IANS): Two primary schools were closed on Monday in Melbourne after some students tested positive for the novel coronavirus, authorities said.

The Department of Health and Human Services (DHHS) confirmed in a statement that two students at St Dominic's School in Broadmeadows were infected with COVID-19 and one of them was already infected while attending classes, reports Xinhua news agency.

"Testing will be undertaken for students and teachers who were at the school from May 26 to June 3," it said.

In response, the school will be closed for three days to enable contact tracing and deep cleaning.

Pakenham Springs Primary School also in Victoria state was shut down on Monday after two students contracted COVID-19.

The school required all students and staff who have attended the school to remain at home while contact tracing is underway.

Victoria state recorded 12 new COVID-19 cases on Sunday. All the positive cases among students were linked to an extended family outbreak in Melbourne's northern and southeastern suburbs.

Another outbreak was identified with two new cases linked to a patient of Monash Health.

One of the new cases is a healthcare worker. The health service is racing to contact all staff and patients who may have been close contacts of the healthcare worker.

In addition, a young woman who attended Black Lives Matter protest in Melbourne on June 6 also tested positive for the virus.

The source of infection is still under investigation, but at this stage there were no links to the previous infected patient who attended the protest.

Victoria's Chief Health Officer Brett Sutton urged anyone who attended the march to remain vigilant and should isolate at home and get tested if symptoms develop.