Bega Valley Public School was open on Monday despite an average of one in three children staying home each day during the pandemic so far.
By Monday more than half the school's students were absent, and 15 per cent of teachers did not go to work, with tailored learning from home packs ready for all students.
On Monday, NSW Premier Gladys Berejiklian encouraged parents to keep their children at home "for practical reasons", although "no child will be turned away from school".
Ms Berejiklian said around 30 per cent of children statewide were already staying away from school last week.
One Bega doctor, who posted on social media their children will be learning from home from this week, said social isolation is crucial early after infection detection. The doctor said they were concerned schools are not set up to implement appropriate social distancing and hygiene requirements.
Prime Minister Scott Morrison told the public on Sunday night his position on schools remaining open had not changed. Mr Morrison said in Parliament "there is not much known" about COVID-19, likening the economic effects as potentially similar to the Great Depression, as he outlined a slowing of society for at least the next six months.
Meanwhile, as the COVID-19 pandemic saw a nation-wide shutdown of all but essential services on Monday, two Bega Valley residents tested positive for the virus over the weekend.
The Southern NSW Local Health District confirmed on Sunday a number of residents had tested positive, and anyone they came in close contact with is in the process of being identified so they can take the necessary steps to avoid further transmissions of the virus.
A Tura Beach resident is now in 14-day self-isolation after testing positive. Little is publicly known about the case, other than they tested positive after returning to Australia after travelling overseas.
A woman from Merimbula who the district said contracted the virus after attending a wedding interstate is now also in self-isolation.
The two were among six in the health district to test positive over the weekend.
Meanwhile, the federal and state governments have imposed stricter social distancing measures.
Only hospitals, workplaces, construction sites and public transport have avoided a nation-wide shutdown, with all pubs, clubs, indoor sporting venues, casinos, places of worship and cinemas forced to close on Monday, while restaurants and cafes can only offer takeaway options.