A number of incidents were reported in the village of Strathfoyle including a sinister message targeting Mark H Durkan which was accompanied by a drawing of crosshairs.
“Mark Durkan will be got,” it read.
Other graffiti stated “Mark Durkan tout” and “Huns out”.
The PSNI said that at around 8.10pm on Saturday a bus that had broken down at the junction of Clonmeen Drive and Temple Road had a window smashed.
Earlier, just before 8pm, reports of antisocial behaviour were reported in Deramore Drive where a door was ripped off a derelict property.
Then just before 10pm on Sunday it was reported graffiti had been daubed on a bus shelter in Clonmeen Drive.
Graffiti was also daubed on a nearby defibrillator unit.
PSNI Chief Inspector Yvonne McManus said some of the recent activity has been directed at a local political representative.
“It is unacceptable when those involved in our political process become the subject of abuse or threats,” she continued.
“This will be thoroughly investigated and we will explore all lines of enquiry.
“The Police Service remains committed to doing everything we can to ensure our elected representatives can live and work free from harassment, intimidation or any other form of criminality.”
Ms McManus said the “serious incidents” are having “a distressing impact” on local residents.
“We have been speaking with local residents in Strathfoyle, and we know this activity is not welcomed in the area, or is it representative of those living in the community,” she added.
“We will continue with a visible presence in the area with our Neighbourhood Policing Team officers on patrol and we will robustly investigate reports made to us, or that come to our attention.
“The actions of those involved could result in someone being seriously injured.
“It has to stop.”
Mark H Durkan
Over the weekend Mr Durkan said he was having to answer questions from his children about why their father would “be got”.
“I’ve lived in Strathfoyle nearly 10 years now and it has been a brilliant home for me, Anne and the children. We love it here,” he wrote on Facebook.
“On a professional level, I have worked extremely hard for the area and have been integral to the delivery of many improvements – the greenway, a state-of-the-art new playpark, supporting a very active community sector, countless wee cases on roads, cleansing and housing. I think it’s fair to say I’ve done a good job for the area.
“I was most disappointed, therefore, to come across this graffiti at the bus stop this evening.
“My children are asking why I ‘will be got’ and who is going to get me.”
The SDLP representative said he suspected the graffiti was in response to him challenging a group of young people in the area after a Translink bus had windows smashed on Saturday night.
Mr Durkan said the attack was the seventh incident in just over a year in which bus windows were smashed.
Police have vowed to continue to meet with partner agencies and representatives and have sought to reassure the community they are committed to working together.
Residents with concerns and have been urged to report them by calling 101 or 999 in an emergency.