Derry City and Strabane District Council is also asking people to help identify owners who fail to clean up after their pets in the City Cemetery.
Owners can be fined £80 for failing to clean up their dog mess.
Council staff are now monitoring the cemetery, the council said.
Anne-Marie Watkins said she has raised concerns to council after twice discovering dog foul on her infant daughter’s grave.
“It is hard enough to leave your baby here without the added stress of this,” she told BBC Radio Foyle’s The Mark Patterson Show.“It makes me so angry. This is not stray dogs, this is where owners have left them off the lead and let them run around people’s final resting places.”
Gary O’Neil told the BBC he has witnessed pet owners “use the cemetery grounds and graves as a play area for dogs”.
“They are playing ball games, fetch over the graves, I’ve seen dogs with parts of flowers in their mouths.
“It is quite upsetting, especially for people dealing with loss.”
A council spokeswoman said council staff regularly monitor the city cemetery “with regard to dog fouling and advise owners of their responsibilities”.
“Council has installed additional dog fouling bins and dog fouling signage within the cemetery. The location of bins and signage is reviewed regularly to ensure problem areas are sufficiently covered,” she said.
Derry and Strabane Council defended its record on dog fouling after issuing just 22 fines despite receiving more than 5,000 complaints in 2018.
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