The Most Rev Bishop Donal McKeown was speaking after it was announced religious services will be allowed to resume in the North of Ireland in time for Easter in two weeks time.
Churches in the Republic have yet to be given a date for resuming their services.
It has led to concerns that those in border regions may decide to travel into the North of Ireland around Easter to attend Mass.
Bishop McKeown said that while he accepted the North of Ireland was in a better position with the virus than in the Republic, he would not stop anybody from attending Mass.
He acknowledged the issue could cause “all sorts of problems”, with Derry neighbouring Donegal.
The area has in the past been the worst affected in the whole of the island of Ireland.
Bishop McKeown said it was not simply a case of people “suddenly deciding to go to church in the north” at Easter.
“The border is crossed innumerable times a day by cars for all good reasons, including work. So, people may want to come to church in the north but until they stop them at the doors of Sainsbury’s, I’m not going to stop them at the door of the cathedral,” he told RTE.
“I think that model of a much more mature relationship between Government and civic society will probably lead to less reaction against things being imposed,” Bishop McKeown said.
“I think if there’s a mature relationship between civic society and those who are responsible for taking decisions, you probably get better outcomes and I think that has come through, even though the Executive in the north is seen as very divided, they’ve succeeded in managing this very well.”
The Archbishop of Dublin has called for an all-island approach to tackling the issue.
Archbishop Dermot Farrell said he believed freedom of religion was currently being restricted in the Republic of Ireland.
“We’re always talking about an all-Ireland approach, and I would like to see an all-Ireland approach to the situation down here where churches can take that decision,” he said.
“I’m asking in the unrolling of restrictions that we be allowed to open along with other things that will be allowed to open”.
Archbishop Farrell said it was “grossly unfair” that people where unable to worship, while other places remained open with “little to no social distancing”.
Catholic Bishops in the North of Ireland’s Catholic bishops announced a “cautious return” to public worship ahead of Holy Week and Easter.
In a statement, the bishops said individual parishes and Covid-19 support teams must carry out a “thorough risk assessment” before returning to public worship from next Friday, March 26.
Church of Ireland bishops have also confirmed the resumption of in-person worship from Good Friday, April 2 and the Methodist Church said it looked forward to a careful return to in-person services from Good Friday.
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