The head of police in Strabane has asked the Co Tyrone town council's Sinn Féin chairman to meet him to discuss the desecration of graves of three IRA members.
The request was made after Jarlath McNulty accused police of destroying wreaths and flowers on the graves of the men, who were shot dead by British soldiers 20 years ago.
On Sunday, Sinn Féin president Gerry Adams led an event to commemorate the killing of brothers Michael and David Devine and fellow Strabane man Charlie Breslin.
Mr McNulty said: "A large number of wreaths on the graves of three volunteers were broken and scattered over a wide area. The vandalism was discovered this morning (Monday) and local people are convinced that it was carried out by members of the PSNI who were seen in the graveyard last night."
He said while the wreaths and flowers could be replaced, the desecration compounded the suffering of the Breslin and Devine families.
Responding to the allegation, Superintendent Raymond Murray said the desecration of any grave was despicable and should be condemned in the strongest possible terms.
"It is important that the allegation is thoroughly investigated to ensure that any wrong-doers are identified and to ensure that any unfounded allegations against the police are dismissed," he said.
Mr Murray said he would welcome an opportunity to meet Mr McNulty to discuss the matter and urged anyone with information to contact police in Strabane or the Police Ombudsman's office.