A Sinn Fein MP has hit out after vandals damaged 19 war graves at Belfast City Cemetery.
The PSNI believes the gravestones were targeted some time between 7pm on Monday and 1pm on Tuesday.
The force issued an appeal for anyone with information to get in contact.
PSNI Inspector Andrew McConville said: "Damage to any grave is absolutely despicable. A graveyard is a place where people come to pay their respects.
"This behaviour and the destruction of graves will have a significant impact on individuals, families and communities.
"We have launched an investigation but need help from the community to bring those responsible before the courts."
The cemetery, at the junction of the Falls and Whiterock roads in the west of the city, is maintained by Belfast City Council.
Paul Maskey, the Sinn Fein MP for the area, condemned those behind the latest desecration of graves at the cemetery.
"This is absolutely disgusting behaviour and it's totally wrong that some people feel the need to go and damage the graves of anyone," he said.
"Graveyards are a place of sanctuary for people to go and pay respects to their loved ones.
"I'm sure those behind this wouldn't like to see this sort of damage happening to their own relatives' graves, so I would call on those responsible to stop this type of activity.
"In my view, they are absolutely pathetic and I don't know what reason or kick they get out of it."
West Belfast People Before Profit MLA Gerry Carroll also hit out at the vandals.
"I totally condemn the attacks on grave headstones," he said.
"Graveyards should be a place for people to mourn and express sorrow for lost loved ones.
"They also offer people the chance to learn about the history of our city and communities, as is the case with the war graves.
"These attacks are pointless and offer nothing to people in west Belfast. I would strongly appeal to those involved in the attacks to cease from doing so."
Police urged anyone who saw any suspicious activity in the City Cemetery from Monday evening through to 1pm on Tuesday, or who has information that could assist the investigation, to contact officers on the non-emergency number 101, quoting reference 829 11/08/20.
Information can also be provided anonymously to the Crimestoppers charity via the telephone number 0800 555 111.
Belfast City Cemetery contains a plot with 274 Commonwealth war graves containing personnel who served in the Second World War and 296 from the First World War.
In recent years graves at the cemetery have been the target of repeated anti-social behaviour and attacks.
Last October damage was caused to 12 Commonwealth war graves in two separate attacks.
Two months later the Commonwealth War Graves Commission revealed that damage caused to 26 graves in the last year would cost almost £17,000 to repair.
In 2016 13 Jewish burial plots were also vandalised.