Unionists were outraged after a republican wielded a replica machine gun during a commemoration ceremony yesterday.
Democratic Unionist Junior Minister Jeffrey Donaldson said the march in honour of the H-block hunger strikers had been no excuse to parade the weapon.
Hundreds of republicans in Derry yesterday commemorated the 10 hunger strikers who died in Long Kesh prison in 1981.
It was the first time the annual event had been held outside Belfast.
"I think it is wholly inappropriate that people should display any kind of weaponry, whether it is replica or not," said Mr Donaldson.
"Symbolism like this should not be used, particularly from our party's perspective."
Sinn Fein defended the marchers' decision to parade the replica weapon and said its presence had a historical significance.
"Families of the victims who were killed through collusion, would have decided to have the replica in the display," added a party spokesperson. "Any criticism is typical of unionist denial around collusion and death squads."
About 300 people marched from the Rosemount factory in Derry to the republican monument in the City Cemetery yesterday.
A large-scale security operation was mounted by the PSNI, as the parade marched along a route that took in the houses where wakes had been held for hunger strikers Patsy O'Hara and Michael Devine.
Wreaths were laid by the INLA, the Irish Republican Socialist Party, the family of Patsy O'Hara, the 32 Country Sovereignty Movement and Oglaigh na h'Eireann.
Five of the hunger strikers came from Derry -- Patsy O'Hara and Michael Devine lived in the city and Francis Hughes, Tom McElwee and Kevin Lynch came from the county.