Locals who witnessed the so-called political wing of the New IRA marching through their area have said it is "not wanted" in the community.
Armed detectives monitored around 200 members of Saor- adh as they marched through Sallins, Co Kildare, for a Wolfe Tone commemoration at Bodenstown cemetery yesterday.
Led by convicted IRA bank robber Brian Kenna, groups of men and woman from across the country walked the 2km route wearing black trousers, white shirts, black berets and sunglasses.
The parade also included two marching bands dressed in military garb.
However, local woman Frances Walsh told the Herald that Saoradh is not welcome by locals in the community.
"For years, we've watched groups like these walk through the town. We have peace now, and it really bugs me to see them, especially when they cover their faces," she said.
"I would like to tell them to go on their way because they're definitely not wanted here.
"I think they're quite delusional and stuck in the past while the rest of society has moved on."
Saoradh means "liberation" in Irish, and the group describes itself as a revolutionary Irish republican party. It has the support of the New IRA, which admitted responsibility for journalist Lyra McKee's murder in April.
Speaking to the Herald, Saoradh leader Kenna (58) claimed the organisation has grown since Ms McKee was shot dead during rioting in the Creggan area of Derry.
"It's very, very strong and continues to grow," he said. "You can see a lot of young people here, a mix of people from all over Ireland. We're getting stronger."
Kenna described Ms McKee's murder as tragic, but "a con- sequence of the fight against British rule in Northern Ireland".
"Saoradh had absolutely nothing to do with Lyra's death, we had no role in it whatsoever," he said.
"We said her death was tragic and have nothing to add to that."
"We understand how and why Lyra McKee died when we look at the reasons why people are continually opposing British rule in Ireland," he added.
"It's a very tragic consequence of the fact that there remains an armed force of occupation in this country."
In April, there was widespread condemnation for Saoradh after it held a demonstration outside the GPO over the Easter weekend less than 48 hours after Ms McKee was murdered.