The Parish Priest of Portlaoise in Co Laois has called for the limit of 10 people at a funeral to be relaxed.
Monsignor John Byrne said the current restriction around the celebration of rituals is very difficult.
Under Level 5 measures, only 10 people are permitted to attend a funeral.
He said: "I would really like to see some alternation of that.
"There is an arbitrary figure of 10. Our parish church is a very, very big church. I would like to see it moved to a figure taking account of the size of a church but equally taking an account of the size of a family."
Monsignor Byrne told RTÉ News that he would like to see the limit increasing to include the direct family members of a person who has died.
"I would mean by that spouse, partner, children, grandchildren, brothers and sisters. Very often in an Irish context people are members of a family of 8 or 9 and they have 4 or 5 children and they have grandchildren and daughters-in-law and sons-in-law."
He said the current arrangement is "piling another real difficulty upon a very, very stressful and distressing situation".
Monsignor Byrne also said it is a very difficult time now for families who are bereaved.
He said "all of the usual supports and psychological aids that we have built up around funerals with friends and families gathering and telling stories, comforting each other, all of those things have been a great help to communities in grieving traditionally in Ireland and they have all just been withdrawn".
He also said the period coming up to a death is extremely difficult.
"If it's a Covid death there is no visiting in the hospital or nursing home, there is no holding hands. And there is that awful anxiety that your loved one is dying and you can't be there with them."
Monsignor Byrne said "there is no good time to be burying your dad or your mam or your brother or sister but this is absolutely the worst of times".
He said he is seeing funerals of coronavirus patients more frequently in the last number of weeks.
"We have celebrated more Covid funerals in the last 3 weeks, than we celebrated in the previous 12 months since the pandemic began. And we are aware of parishioners who are seriously ill with Covid at the moment and we pray for their recovery but not all are going to recover. That is the unfortunate reality."
Monsignor Byrne said it is "really a tragic time" and he said "it is affecting us now much more than at any period since the pandemic began".