The police have been asked to increase patrols around the Londonderry's Peace Bridge after a number of reportedly sectarian incidents near the landmark.
The DUP has met officers over recent attacks there and at St Columb's Park.
In one incident, the party said a community worker and a friend were assaulted after going to help a young man wearing a Northern Ireland jersey.
In another, the father of a Protestant man beaten up near the bridge said he had no doubt the attack was sectarian.
Allister Gault told the BBC his 21-year-old son was knocked unconscious in the mugging last week.
The young man had been attending the birthday party of a Catholic workmate in the city centre and was making his way home when a group of youths targeted him and called him sectarian names.
"He decided to walk home as he couldn't get a taxi," Mr Gault said.
"Two guys linked unto him and got him onto Browning Drive and gave him a beating and mugged him and took his wallet.
"He was knocked on the head and knocked unconscious and had a black eye."
Mr Gault said his son was left shaken by the ordeal and may have sustained a cracked rib.
"My son isn't a sectarian person and it is so sad seeing things like this happen in the town."
The Peace Bridge was built as symbol of reconciliation linking the mainly nationalist and unionist sides of the city.
The DUP met senior officers on Monday to underline its concern at a number of recent incidents which the party described as a major cause for concern.
It asked for more visible patrols around the bridge and the park.
DUP councillor Gary Middleton said that he got reassurance from the police that they would be committing additional resources to St Columb's Park.
"We did stress the need for a wider strategy. Recently we have seen an increased amount of tension in the area," he said.
Sinn Féin has said the trouble should not undermine the good cross community work going on in Derry.
PSNI Supt Gordon McCalmont has made an appeal for potential victims of the attacks to report the crimes to police.
"We want people to come forward to talk to us," he said.
"This sectarian element has come to the fore in the past week and it is causing us concern that somebody might be in the background orchestrating this.
"We must make the park an uncomfortable place for anyone with criminal intent or sectarian motives."