Edwin Poots has called for the reopening of cemeteries.
The Agriculture, Environment and Rural Affairs Minister said the "draconian measures" were "initially taken to drive a message about social distancing home", and praised the public for their response to the advice.
But Mr Poots told this newspaper he believed cemetery closures "should only ever have been a very short-term measure".
"I believe that message has been accepted and respected by the public," the DUP MLA said.
"We as the Government need to treat the public with respect as well. To me, that means that we should be facilitating people who want to visit the graves of their loved ones. (Being unable to is) understandably causing huge pain and anxiety for many."
Mr Poots, a former health minister, also called for an urgent decision on the matter.
"We're in a situation where the surge was to take place between April 2 and 20," he said.
"We've reached that point now and there's a reduction in the number of people being admitted to hospital with coronavirus. It's not a time to be complacent, nor is it a time for people to start doing silly things.
"However, visiting graves is important and it's something where people can practise good social distancing.
"In my opinion, therefore, it should be permissible."
Mr Poots also defended the decision to reopen off-licences, saying it was based on the premise that "people would be flooding supermarkets to buy alcohol" and "the consequence of that would be that others wouldn't have been able to buy food".
"There was good reasoning behind that and there's good reasoning behind allowing people to visit graves" Mr Poots said.
He also stressed that not being able to visit cemeteries was "causing a degree of mental anguish to people".
The Lagan Valley MLA said there was a "harshness" to the decision that he described as "quite cruel".
"Coronavirus has been cruel and we don't want to see more graves, but I think we can legitimately exercise a degree of relaxation on this issue," the Agriculture Minister added.