She has asked the police ombudsman, Nuala O'Loan, to investigate the incident which happened in the Brandywell area of the city during disturbances after the Apprentice Boys annual march last month.

The 73-year-old woman was too upset at the death of her pet to speak to the Sunday Tribune, but Sinn Fein councillor Patricia Logue accused the PSNI of animal cruelty.

"The dog, which was a family pet, was outside the pensioner's home when a PSNI Land Rover mounted the pavement and deliberately ran it over, killing it instantly, " Logue said.

"The Land Rover sped off but returned several minutes later. The dog's owner stopped it and told the driver he had killed her dog. The driver replied, 'So what?' while the rest of the occupants laughed as the driver hid his number on his lapel."

Logue claimed the Land Rover had been driven "in a reckless manner" around the estate and could have endangered local children.

"Again, the PSNI have shown complete disregard to the rights of nationalists and this is another example of how little has changed in terms of policing, " she said.

"Whether it is terrorising children, or killing family pets, the PSNI act with impunity without fear of being held to account."

The PSNI described the incident as "unfortunate". A spokesman said: "Following the Apprentice Boys parade, police were in the Brandywell attempting to make an arrest for riotous behaviour when, unfortunately, a dog ran in front of a Land Rover and was injured.

"Police stopped the vehicle and attempted to deal with the situation. However, a hostile crowd gathered and tried to pull officers into their midst. In order to avoid further tensions, police withdrew from the area."

A spokesman for the police ombudsman's office said a complaint had been lodged about the incident and would be investigated.