There are also plans to bring forward Thursday’s scheduled executive meeting on tightening restrictions as infection rates continue to spiral.
The meeting could be held as early as later on Monday, October 12, it has been suggested.
Speaking on Monday, Education Minister Peter Weir said it was “critical” schools remained open.
There has been speculation they could close for an extended half-term break.
Thornhill College in Derry is now closed all this week for a deep clean over a spike in Coronavirus cases.
“There is a strong need as we move ahead to ensure that our children don’t suffer further through loss of learning,” the minister told BBC Radio Ulster’s Good Morning Ulster programme.
“There is a need to protect education, schools themselves don’t seem to be particular spreaders.
Mr Weir said he did not think schools closing would be “in anyway helpful”, saying: “Even short term closures would damage children’s education.”
The North of Ireland’s political leaders spent Sunday having discussions with public health experts.
First Minister Arlene Foster, Deputy First Minister Michelle O’Neill and Health Minister Robin Swann took advice from the local chief medical officer and chief scientific adviser.
“Heavier restrictions are not inevitable,” said Mrs Foster in a video posted to her Twitter account on Monday.
The first minister said the executive will have “big decisions to take this week”.
“It is hugely disappointing that a small minority still think that [restrictions] don’t concern them,” she said.
Mrs Foster urged people to go “back to basics” by engaging in social distancing, maintaining good hand and respiratory hygiene and wearing a mask “in the appropriate places”.
It comes as 1,066 new cases were reported by the Department of Health on Sunday, with one further death.
That was the North of Ireland’s second-highest daily number of reported cases, after 1,080 positive cases were recorded on Friday.
There were 231 positive cases in the Derry and Strabane council area.
Fresh restrictions in the Derry and Strabane council area on the hospitality sector have been in place a week now with no sin of infections falling at yet.
There are now 137 inpatients with Covid-19 in hospitals here, 19 of whom are in intensive care.
The latest figures show 5,909 people have tested positive over the past seven days – more than 30% of the total number of who have tested positive during the pandemic.
Sunday’s figures for the Republic showed 814 new cases in the past 24 hours, with two Covid-19 related deaths.
That brought the total number of Coronavirus cases in the country to 42,528, with a death toll of 1,826.
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