"It is not necessary for the entire class to self-isolate... only students sitting at the same desk, those within 2 metres and those who travelled together (with the infected student) for more than 15 minutes," Capak told a regular press conference by the national COVID response team.
A document is being prepared that will explain those self-isolation rules, he said.
Of the 1,291 new cases of coronavirus in the past 24 hours, 260 were schoolchildren or 20%, he said.
There are currently 2,038 cases of infected children aged between 7 and 18 and 10,349 are self-isolating. There are also 215 teachers infected and 46 other personnel in schools.
"We are still not considering COVID certificates in the school system for the time being but it is clear that that possibility remains on the table," he said.
He warned that over the past week, 73% of hospitalised COVID patients, 83% of those on ventilators and 76.5% of fatal cases had not been vaccinated.
There has been some increased interest in vaccination and in the past 24 hours, 5,800 people received the first dose, said Capak.
Jab, test or you can't work
As far as introducing COVID certificates for workers in the health system as of 1 October, Health Minister Vili Beroš said that staff who are not vaccinated will have to get tested twice a week. Initially, this will be free.
"If they do not wish to get tested, they will not be allowed to work and that will be recorded in their working hours. This will lead to problems in the system because replacements will have to be found and, because their absence will be considered unjustified, they will not get paid," he warned.
Anyone working on hospital grounds, including delivery and repair people and people working in hospital cafes, will also have to have a COVID certificate, Beroš said