DUBLIN — Amid widespread condemnation and anger at the killing of a journalist in Northern Ireland last week, a paramilitary group calling itself the New Irish Republican Army took the unusual step on Tuesday of admitting responsibility for the act and offering its “full and sincere” apologies to her partner, family and friends.

The admission came as the Police Service of Northern Ireland announced that it had arrested a 57-year-old woman in connection with the shooting, which occurred Thursday night in the city of Londonderry. Two teenage men who were arrested on Saturday for questioning were later released without charge.

The journalist, Lyra McKee, 29, died after she was hit by a pistol bullet fired at the police during a riot in the strongly Roman Catholic and nationalist Creggan area of Londonderry, which republicans generally call Derry.

She is believed to be the first journalist killed in the line of work in the United Kingdom since 2001, and her death is seen as a worrying echo of the Troubles of 1968 to 1998, when more than 3,500 people — many, like Ms. McKee, nonaligned civilians — died in violence pitting mainly Catholic republican gunmen seeking a united Ireland against the police, British soldiers and mainly Protestant gangs defending Northern Ireland’s union with Britain.