The City Cemetery in Derry is run by the council.
Derry City and Strabane District Council is to write to local churches to ask them to waive burials fees during the coronavirus pandemic.
The Mayor, Michaela Boyle, recently suggested that the council should waive the burial fees for its own cemeteries during the pandemic.
Her proposal came before a meeting of the council today for a final decision.
A report prepared for the meeting stated that waiving the burial fees over a six month period could cost the local authority around £78,000.
Given the costs involved, a number of councillors told the meeting that they could not support the proposal.
Among those who raised concerns was independent councillor Sean Carr, who is also an undertaker.
Cllr Carr said the council's proposal would only affect families with loved ones buried in council-run cemeteries.
However, he claimed that 50% of local people would choose to be buried in church-run cemeteries, such as Ardmore or Melmount in Strabane.
Cllr Carr suggested that if the council waived its burial fees, it could be discriminating against the families of people who were buried in church cemeteries.
The meeting was told that there was a grant available for people on specific benefits to help with funeral costs.
Several councillors suggested that by waiving its burial fees the council could simply be saving the government money instead of the families involved.
There was also concern expressed at the meeting about the period over which the waiving of the fees would be in place.
Strict restrictions around how funerals are operated were introduced on March 28 in response to the coronavirus pandemic.
Today's meeting was told that there had been a 'small number' of coronavirus-related burials in Derry before that date.
After a lengthy debate at the meeting, SDLP councillor Martin Reilly proposed that the council waive burial fees for one month, backdated to March 28, and then review its decision.
Cllr Reilly said that the families of people whose deaths were linked to coronavirus before March 28 should also not have to pay the fees.
The proposal to waive the burial fees for this period was then put to a vote.
It was supported by 24 councillors, including the representatives of Sinn Fein, the SDLP and the DUP.
Six councillors abstained during the vote, with one councillor, Aontu's Anne McCloskey, voting against it.
Cllr Boyle thanked the councillors for supporting her proposal.
She said she understood the concerns about the cost to the council, but felt that it was the 'humanitarian' thing to do to help families through this difficult time.
Cllr Boyle asked council officers to write to local churches to ask them, in light of the council's decision, to also temporarily waive burials fees for their own graveyards.
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