A high school and primary school in south-west Sydney were closed on Tuesday after three students were diagnosed with COVID-19, while NSW has recorded 12 new cases.

Bonnyrigg High School and Greenway Park Public School were closed for deep cleaning and contact tracing, and students have been advised to self-isolate.

“All students will undertake at home learning tomorrow,” Bonnyrigg High School said on its website on Monday night.

Greenway Park Public School said students will also learn from home for the day after two students tested positive to COVID-19. Further advice was to come later on Tuesday.

NSW Health has asked anyone linked to the schools who has been unwell or has respiratory symptoms to get tested for COVID-19.

• See a full list of NSW venues associated with confirmed cases here

NSW chief health officer Dr Kerry Chant said the three infected students were associated with the Mounties Club cluster in Mount Pritchard.

NSW recorded 12 new COVID-19 cases from 12,876 tests in the 24 hours to 8pm on Monday. One case is in hotel quarantine and none are from an unknown source.

Six COVID-19 patients in NSW are in intensive care and five are ventilated.

Two of the three ill students are included in Tuesday’s numbers.

Meanwhile, NSW Premier Gladys Berejiklian has warned NSW could toughen border restrictions with Victoria, saying: “If we have to do more, we will.”

NSW reported 13 new COVID-19 cases on Monday – four returned travellers from overseas or Victoria, and one person with no known source.

Four cases announced on Monday from the weekend included a 52-year-old woman, her son, daughter-in-law and their baby, having recently returned from Melbourne to Wagga Wagga in the NSW Riverina and gone into self-isolation as required.

The NSW government has strongly recommended people wear masks in high-risk situations as the state enters what Ms Berejiklian labels a “critical phase”.

The Premier said she carried a mask at all times and again urged public-facing workers, worshippers, people living near community clusters and those in enclosed spaces to wear face masks.

However, masks will not yet be made compulsory in NSW.

NSW Health on Tuesday said the Thai Rock Wetherill Park cluster numbered 103, while the cluster at Potts Point in inner Sydney numbered 28.

“It is important to reiterate that while most cases in the past week have been associated with local clusters and close contact with known cases, some have not been linked, representing unknown chains of transmission,” Dr Chant said.

She urged anyone in isolation to observe the full 14 days self quarantine as “early testing may not detect an infection”.