Speaking in the Dáil on Tuesday evening, Mr Adams said that the death of Garda Adrian Donohoe evoked memories of the 1996 killing of Garda Jerry McCabe and wounding of Garda Ben O'Sullivan.
Garda Donohoe was shot dead without warning as he escorted a cash delivery van in the rural village of Lordship on Friday, by a gang who made off with €4,000 and sparked a cross-border hunt.
Mr Adams said he didn't know him personally, but knew many people who did.
He expressed his sympathies to his family, friends and colleagues and expressed "solidarity and sincerest condolences" to his wife and children.
"This killing has shocked the entire community, especially in the very closely knit Cooley area in County Louth and in South Armagh," Mr Adams said.
"He was a valued and widely-respected member of our local community and there is a deep sense of shock and loss."
Prior to Friday's fatal shooting, Jerry McCabe was the last Garda officer to be murdered - when he and colleague Ben O'Sullivan were shot during an attempted robbery of a postal van in Co Limerick.
I want to apologise to Mrs McCabe and the McCabe family, and to Garda Ben O'Sullivan, and to the families of other members of the state forces who were killed by republicans in the course of the conflict.
Gerry Adams, Sinn Féin
"I am very sorry for the pain and loss inflicted on those families. No words of mine can remove that hurt. Dreadful events cannot be undone," Mr Adams said.
"I want to restate that the resolve of Sinn Féin, and of the majority of Irish people, is to ensure that there is never ever a recurrence of conflict.
The Sinn Féin president added: "Members of An Garda Síochána do a dangerous job. They take risks for all of us. Adrian Donohoe showed great courage when he confronted armed criminals at Lordship. He died in defence of other citizens.
"I want to appeal to anybody with any information about this crime to co-operate with the gardaí or the PSNI. I hope that those responsible are speedily brought to justice."
William McCrea, the DUP's South Antrim MP, has called on Mr Adams to apologise to the families of all police officers and soldiers who were killed in the Troubles - not just those in the Republic.
While Mr McCrea welcomed the apology, he said many families who had loved ones murdered are crying out for justice.
"Just as Gerry Adams has apologised for the PIRA murder of Republic of Ireland security forces, he should do likewise for those RUC officers and soldiers who were murdered. It would be grossly offensive if Gerry Adams differentiates between the murder of a Garda officer and the murder of an RUC officer or a UDR soldier.
"I am very mindful that whilst many families would welcome an apology, they still cry out for justice. Too many families have never seen anyone brought to justice for the murder of their loved one."
Meanwhile, investigations are continuing into the murder of Garda Donohoe and An Garda Síochána have renewed appeals for information - particularly in relation to the burnt-out car found in Co Armagh.
The navy Volkswagen Passat was stolen during a burglary at Clogherhead in Co Louth overnight on 22nd/23rd January - the night that a large funeral was taking place.
"Anyone who may have noticed the car in the day or hours leading up to Friday last, or who may have seen this car in the Bellurgan or Keady areas, or indeed who may have any information about this car, is asked to contact the incident room at Dundalk Garda station," a spokesman said.
Anyone who noticed any suspicious activity in the vicinity of Lordship Credit Union in Bellurgan, between 7.30pm and 9.30pm on Friday 25 January 2013, or in the days preceding, is also asked to contact gardaí.