A call to reopen cemeteries has divided Stormont’s parties.
Council-run graveyards were closed in Northern Ireland last month as part of the coronavirus movement restrictions.
The DUP and UUP support reopening, while Sinn Fein and the Alliance Party have said they remain opposed.
First Minister Arlene Foster said the ministerial executive at Stormont would have more discussions about whether to reopen cemeteries during the lockdown.
She said visiting could be allowed during limited hours and while making sure social distancing was in place.
She admitted other colleagues had “justifiable concerns”.
Deputy first minister Michelle O’Neill said restrictions will be lifted when possible but the infection was still active.
“Ultimately this is still about saving lives.”
She added: “We are still in the public health crisis but we and the Executive have to plan for what comes down the line.”
Former Ulster Unionist Party leader Mike Nesbitt said he did not believe keeping cemeteries shut was a price worth paying.
He said: “I know I could visit my father’s grave at Roselawn (near Belfast) and the authorities could ensure social distancing is maintained in a way it is not maintained at our supermarkets on a daily, hourly or minute-by-minute basis.”
Sinn Fein’s Executive Office junior minister Declan Kearney said restrictions were in place to protect people.
He told the Assembly: “I and Executive colleagues understand how difficult it is that members of our families, friends and community are being denied solace which moments of reflection at gravesides can provide, but that is the price we must pay.
“We have not beaten Covid-19. No other interest can take primacy over our public health.”
He said: “The impact of the lockdown has been particularly hard on those experiencing the trauma of losing a loved one.
“The way we process grief and deal with the death of someone close has been coldly suspended by the coronavirus outbreak, making experiences of loss more difficult to bear.
“We have a duty, therefore, to approach these matters with sympathy and compassion.”
He added that the need of people to grieve and visit their loved ones is powerful.
“But it must be balanced with our duty to protect public health, restrict transmission of this virus and prevent further loss.”
A Department of Health statement said ministers are due to review the regulations before May 9.
“Any changes to the current position will be a matter for the entire Executive.”