Irish politicians and clerics have turned Easter Rising commemorations into a platform to condemn dissident republicans for the killing of Lyra McKee.

They used the 103rd anniversary of the 1916 rebellion against British rule, traditionally a day to celebrate the republic’s founding fathers, to lambast the New IRA and its political affiliate, Saoradh, over the shooting of the journalist in Derry on Thursday.

Josepha Madigan, the culture minister, told a crowd gathered at Glasnevin cemetery in Dublin to honour those who died during the Easter Rising and reject the journalist’s killers, saying they represented nobody.

Q&A What is the New IRA? Show The New IRA is the biggest of the dissident republican groups operating in Northern Ireland. It has been linked with four murders, including the shooting of journalist Lyra McKee in Derry in April 2019. The group is believed to have formed between 2011 and 2012 after the merger of a number of smaller groups, including the Real IRA, which was behind the 1998 Omagh bombing. Its presence is strongest in Derry, north and west Belfast, Lurgan in County Armagh, and pockets of Tyrone, including Strabane. In January 2019 the group was responsible for a car bomb outside the courthouse in Derry. The explosives-laden car was left on Bishop Street on a Saturday night, and scores of people, including a group of teenagers, had walked past before it detonated. The New IRA also claimed responsibility for a number of package bombs posted to targets in London and Glasgow in March 2019.

The taoiseach, Leo Varadkar, and the Irish president, Michael D Higgins, also took part in commemorations.

Bishop Donal McKeown, the Catholic bishop of Derry, told the BBC that the dissidents were a danger to everybody in the city. “The one liberation they require in that community is liberation from Saoradh,” he said. Saoradh means liberation in Irish.

The rebukes followed a march by Saoradh supporters through central Dublin on Saturday and fresh security alerts in Derry on Sunday.

About 200 people, some in paramilitary dress, marched up O’Connell Street under the gaze of gardaí). Tricolours and banners saying “unfinished business” hung from lampposts.

Taoiseach Leo Varadkar (left) and President Michael D Higgins after the commemoration to mark the 103rd anniversary of the 1916 Easter Rising in Dublin. Photograph: Liam McBurney/PA

Dee Fennell, a national executive member of Saoradh, called McKee’s killing a tragedy and urged those responsible to publicly apologise.

The spectacle of marchers with berets, sunglasses and military garb prompted indignation from some passersby and criticism of authorities for permitting the parade.

Security alerts across Derry on Sunday morning caused road closures and house evacuations in advance of a Sinn Féin parade.

Police have arrested a 39-year-old man and said they were treating the incidents, which included a hoax package left outside the home of a republican councillor, as criminal rather than terrorist incidents. That designation appeared to rule out the incidents as acts of defiance by the New IRA.

The group’s supporters cancelled their own parade, which had been planned for Monday, amid disgust over McKee’s death.

The journalist was shot in the head when a masked gunman opened fire in the direction of police vehicles.