Derry-born Archbishop Eamon Martin made the call in a letter to DUP Education Minister Peter Weir, which said: “We need to fight this virus together.”
Mr Weir had said shutting schools now may be “counterproductive,” adding that he would follow scientific advice.
The political leaders in the North of Ireland are also split over when schools should close.
On Friday morning, Deputy First Minister Michelle O’Neill called for the immediate closure of schools and colleges.
The sudden U-turn came a day after she said the North of Ireland was not at the stage where it needed to shut them.
Later, First Minister Arlene Foster said the policy to keep schools open would stay in place.
Schools, colleges and other public facilities in the Republic have shut due to Coronavirus.
But in the North of Ireland officials have not taken the same steps.
Nine new cases of Coronavirus were confirmed in the North of Ireland on Friday, bringing the total number of cases to 29.
It also emerged that three cases were the result of community transmission – the first cases in which a patient had no known contact with a confirmed case and had not travelled from a country badly affected by the pandemic.
In a letter addressed to Mr Weir and the Council for Catholic Maintained Schools (CCMS), Archbishop Martin said the St Patrick’s weekend provided a “clear window” for parents to make childminding arrangements ahead of closures and for schools to make contingency plans.
“I feel it is important to give very strong consideration to the closure of all schools in the very near future and on a specific defined date,” he wrote.
Speaking at Stormont on Friday morning, Mrs O’Neill said the North of Ireland should “err on the side of caution” and “now is the time for action”.
“Now is the time to ensure that all schools are closed, that universities and colleges are closed and that needs to be done immediately,” she said.
However, the first minister said that, while she understood Mrs O’Neill’s concerns that there’s a different policy in the Republic, she had “to be led by science”.“I can’t answer as to why Michelle has decided she needs to go in this direction.”
Speaking after a meeting with UK Health Minister Matt Hancock and the Chief Medical Officer Michael McBride, tbe North’s Health Minister Robin Swann said he would “continue to be led by the science”.
“At this moment in time, I have no evidence to justify school closures and indeed to do so at this stage may even be counterproductive,” he said.
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