The parties are to hold talks around whether to reopen cemeteries.
Cemeteries are operated by councils and have been closed, except for burials, since the lockdown began last month.
The Assembly has the power to reopen them via legislation.
Many families have called for the decision to be reversed to allow them to visit the graves of their loved ones.
Some have questioned why off-licences remain open while cemeteries have been shut.
Parties are split on the issue, with the DUP and Ulster Unionists in favour of reopening and Sinn Fein and Alliance opposed.
Mid and East Antrim councillor Timothy Gaston said he had been contacted by people "in dismay" because they could not tend to family graves.
The TUV councillor lives in Cullybackey, where an elderly man was seen struggling to climb over a cemetery wall to lay flowers on his wife's grave on Sunday.
Mr Gaston said: "There are a number of people who have contacted me who have anniversaries coming up.
"It's been very raw for them not being able to tidy the graves or lay flowers on them."
First Minister Arlene Foster and Deputy First Minister Michelle O'Neill addressed the division at Stormont's daily media briefing yesterday.
The DUP leader said that while colleagues had "justifiable concerns", her view was that cemeteries should be reopened with social distancing rules.
"I do fully recognise and we all sympathise with the many distressed constituents who have made contact right across the political spectrum who have not been able to maintain graves or visit graves as a result of the regulations," Mrs Foster added.
"Much has been said on the negative impact from lockdown on people's mental health and anguish.
"I think that this is a very good example of that.
"We are not just dealing with the direct harm caused by Covid-19. We come here every day and talk about the number of lives lost to this, but we also have to acknowledge the wider harm that is going on in society as a result of Covid-19."
Deputy First Minister Mrs O'Neill said restrictions would be lifted when possible, but the infection was still active.
She said she recognised the sensitivities of the issue but warned against the reopening of cemeteries.
"We still are in a pandemic, we are not out the other side of this yet," she explained.
"We have to focus very much on the public health message, which is to stay at home.
"Restrictions will only be lifted when it is safe to do so. This is for the public interest."
Earlier in the Assembly chamber former UUP leader Mike Nesbitt told MLAs 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 junior minister Declan Kearney said restrictions were in place to protect people.
"I and my 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," he added.
"We have not beaten Covid-19. No other interest can take primacy over our public health."
SDLP leader Colum Eastwood has written to Health Minister Robin Swann requesting the latest medical and scientific advice from the chief medical officer and chief scientific officer on proposals to open cemeteries.
"The impact of the lockdown has been particularly hard on those experiencing the trauma of losing a loved one," Mr Eastwood stressed.
He said the need of people to grieve and visit their loved ones was powerful.
"But it must be balanced with our duty to protect public health, restrict transmission of this virus and prevent loss," he added.
Mid and East Antrim Council said the reopening of cemeteries in the borough would happen with "immediate effect" when regulations allow it.
"The council will ensure robust social distancing protocols are in place to protect residents and our staff when this happens," it added.
"This is an extremely emotive and sensitive issue. We sympathise with those unable to visit the resting places of loved ones, and understand the deep hurt this is causing."
The Department of Health said ministers were due to review the regulations before May 9. "Any changes to the position will be a matter for the Executive," it added.