The chairman of the Bloody Sunday Trust has outlined its opposition to the re-enactment of the original march through Londonderry.
Tony Doherty's comments follow a backlash against the presence of dissident republican group Saoradh at this year's event.
Mr Doherty, whose father Paddy was among the 13 men killed by soldiers while he was taking part in the civil rights parade on January 30, 1972, said the majority of families who are represented by the trust have had nothing to do with the march since 2011.
This year's event drew criticism because of the participation of Saoradh, considered the political wing of the New IRA, who murdered journalist Lyra McKee in Creggan last April.
Many comments posted on social media took swipes at the wider Bloody Sunday campaign because of the presence of Saoradh, but Mr Doherty said this was misplaced.
"We don't normally court controversy but we want to make it clear that we don't have any association with that march," he said.
"This goes back to 2011 when the majority of the Bloody Sunday families asked the population of Derry to march with them for the last Annual Bloody Sunday march.
"The Bloody Sunday Trust was asked by the families to organise events around civil rights and human rights issues instead, as a commemoration of Bloody Sunday, which we continue to do.
"A small number of families decided to go their own way, but the vast majority of family members abide by the decision taken in 2011 that it was time to bring the march to an end for no other reason other than it had stopped being an effective campaigning tool. The vast majority of families do not take part in this march, nor do they have anything to do with it."
A small number of Bloody Sunday family members, along with others, formed a committee to allow the march to continue, but widened the remit to a March for Justice open to anyone wishing to participate.
Committee member Eamonn McCann said that while he, like others, wished Saoradh was not at the march, the committee would not stop them taking part.
He said: "It is true that less than a year after the murder by dissident republicans of Lyra McKee, many people might think it is inappropriate for dissident republicans to be marching for civil rights, and I would agree with them.
"The fact that I agree with these sentiments does not mean that I can or would want to exclude them (Saoradh).
"I will continue arguing with them, as I do robustly, as I argued down through the years with supporters of republican paramilitarism.There wasn't any specific discussion about Saoradh taking part. The attitude is anyone can join - it is a public march and anyone can join.
"There is a diversity of groups on the march, from Pride to environmental groups like Zero Waste North West, and Saoradh came along too."
Mr McCann added he understood people would be outraged by the presence of groups linked to violence at the march.
"The Bloody Sunday march originally was a civil rights march, which was in effect taken over by republicans and that has been going on for years," he said.
"I cannot speak for the committee, but I can point out there are 12 people on the committee and not one of them would want anything to do with dissident republicans or political violence.
"There is only a minority in the committee who would consider themselves a republican of any sorts - they are civil righters.
"You cannot exclude people from the march, much as you might wish they were not there."