A delegation from the DUP has held talks with the PSNI about how Friday's loyalist parade in Rasharkin should be policed.
Last week, the Parades Commission placed restrictions on the annual Ballymaconnelly parade following trouble at the event last year.
The organisers, Ballymaconnelly Sons of Conquerors Flute Band, wanted to go through the village, then back again.
However, the commission has banned the return parade.
There was minor trouble at the parade last year when some golf balls were thrown at the marchers. Residents also blew whistles and horns.
The DUP delegation included Mervyn Storey and Jeffrey Donaldson.
"It is widely known that there is a small republican core in Rasharkin intent on violence," Mr Storey said.
"This was demonstrated last year by the arrests and prosecutions.
"It is vital that the police take the right approach and ensure that anyone attempting to start trouble is swiftly dealt with."
Later on Tuesday, a delegation from Sinn Fein met the Parades Commission to discuss Friday's parade.
Speaking after the meeting, Sinn Fein's Daithi McKay accused the DUP of "stirring up tensions in the Rasharkin area".
Mr McKay said that this "runs contrary to the mature position adopted by the Residents' Association, who have been working strenuously to reduce tensions in the area".
After the meeting with the DUP, a police spokesperson said: "Police have responsibility to police the Parades Commission's determinations and that these are policed appropriately and proportionately.
"We will facilitate the right of people to parade lawfully and peacefully, as we will facilitate the right of people to protest lawfully and peacefully."