St Ninian's Parish Church in Newtownabbey is expected to close in a few months' time.
The church, which has stood on the Whitewell Road for 51 years, has a columbarium underneath the building for urns containing the cremated remains of parishioners.
Rev Elaine O'Brien said changing demographics in the area meant the church had an ageing congregation "and it's no longer financially sustainable".
"That means the remains have to be disinterred and reinterred elsewhere," she said.
"I have managed to track down some family members but there are still a few that are outstanding.
"We are legally bound to put the advert in local newspapers for three months to see if anyone comes forward."
If the ashes are not claimed, the Church of Ireland rector said they would be moved to the garden of rest at St John's Church on the Shore Road.
"It means that if someone comes along in a few years' time looking to trace their family tree or whatever, they'll be able to find their relatives," she said.
Columbarium, from the Latin columba, or dove, originally referred to a shelter for doves or pigeons.
The term now refers to a site for the "respectful and usually public" storage of urns containing a deceased's cremated remains.
A church that is closing down has issued an appeal for anyone whose loved ones' cremated remains are kept there to come forward.