A council-run cemetery is perceived by some Catholics, nationalists and republicans as "not a welcome place for them", Sinn Féin has said.
The concern was raised about Roselawn cemetery on the outskirts of Belfast following a banner being erected near the site mocking the death of prominent republican Bobby Storey.
His cremation at the site last month was the subject of controversy after several bereaved families were denied the same level of access to services scheduled on the same day.
Police are investigating the banner incident and are treating it as "hate motivated".
Sinn Féin has been granted an equality impact assessment on proposals for a new £18 million crematorium at Roselawn.
At a council committee yesterday, councillor Ronan McLaughlin said he and party colleagues have been contacted by families of recently-deceased people who are "concerned about Roselawn".
"There is a perception within the Catholic, nationalist and republican community that Roselawn is not a welcome place for them," he said.
The Alliance Party and DUP both said they believed the banner was an "isolated incident".
However, all parties agreed that plans for the new crematorium should be subject to an equality impact assessment.
Sinn Féin said was not against the building of the crematorium, but wanted to make sure everyone would feel welcome there.
DUP councillor George Dorrian, the party's group leader on the council, said the recent banner was "reprehensible" but he did not think it was part of a "wider problem".
