One man was arrested after minor scuffles with police as the flame was about to pass the peace bridge linking the divided communities in Londonderry. Nobody was injured. The torch was re-routed by about 100 yards.
SDLP MLA Mark Durkan said: "We support anyone's right to protest but that has been abused here today in Derry. People are just absolutely disgusted that there will be negative headlines for the city coming out of a great afternoon."
Mr Durkan said there had been an agreement not to disrupt the relay. The protest was not aimed at it, but shoving with stewards broke out and police intervened to push the crowd of around 100 - half of them children - back.
A Police Service of Northern Ireland spokeswoman said several dissident republicans were involved.
"Due to a protest that took place at the rear of the Guildhall this afternoon, the torch was diverted past Guildhall Street on to Whittaker Street where it continued on to the peace bridge," she said.
One man was arrested and there were no injuries. The protest has dispersed and was not related to the torch.
Londonderry, where this evening's celebrations were held, has had problems with dissident republican violence and security was tight - an explosive was thrown at police in an attempted murder bid over the weekend. It will be UK City of Culture next year.
The bridge has been built between a disused army base on the shores of River Foyle in a predominantly unionist part of the city and the other, nationalist, side.
The torch started its relay proper from Coleraine, Co Londonderry, and continued through villages and towns including Limavady to Londonderry city. It crossed the River Bann in a boat. Seamus Reynolds carried the torch with an eight-man rowing team. He was picked because of his work in the community.