One of the messages, daubed onto a bus stop in the village of Strathfoyle on the city’s outskirts, were accompanied by a drawing of crosshairs, with the message: “Mark Durkan will be got”.
Others read “Mark Durkan tout” and “Huns out”.
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 ten years now and it has been a brilliant home for me,Anne and the children. We love it here,” he said in a post on his Facebook page.
“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.
“The same group have been responsible for a litany of destruction and intimidation for well over a year. They have the community terrorised,” he said.
“Valiant efforts have been made by various agencies and local groups to tackle this issue and, other than the odd, isolated improvement, the situation is probably worse now than ever as the kids have got bigger and bolder.
“Not only does this endanger those on the bus,not least the drivers,but it threatens the service itself – meaning no late bus for the people of Strathfoyle who depend on it.
“The local shop recently had to employ security because poor staff have been terrorised.
“The playpark, which is the envy of just about everywhere, has constantly been the target of arson and vandalism.”
The former Stormont Minister for the Environment said there had been incidents of hate crime within the estate, with homes of “newcomer and Protestant families” targeted.
“Anyone who ‘speaks out’ has been targeted. Firefighters, police and community wardens are frequently pelted with missiles as they respond to incidents in the area,” he added.
“Last week, I’d my windscreen cracked in an indiscriminate attack – it could have been anyone driving along.
“I’d say it would be a conservative enough estimate to say the cost to the public purse of this wave of destruction has been hundreds of thousands of pounds, nevermind the cost to private citizens of repairing their property.
“What can’t be measured is the damage it has done to people – the fear and anxiety caused to many vulnerable people and families. This has to stop now.”
Mr Durkan said local community groups and the police have tried to resolve the situation and urged anyone with information about the recent incidents to come forward.
“I never want to see young people demonised or criminalised – and the vast majority of young ones here are dead on – but this has long passed ‘boys will be boys’ stuff,” he said.
“By letting things go we are actually letting them down and younger children are coming up thinking that their behaviour is acceptable. It isn’t.
“Local community groups have tried their best.The police have tried but have huge difficulty apprehending those responsible because residents are afraid to give statements.
“I have, until now, made no public commentary on these events as I do not want to besmirch the image of Strathfoyle, my home, and the many wonderful people who live here.
“I would urge anyone with any information about any of the many recent incidents in Strathfoyle to come forward. We want a village that is clean and safe.”
The PSNI have been approached for comment on the incidents.