Without dialogue between Orangemen and residents over contentious marches, clashes like those witnessed at Drumcree will be repeated, the Taoiseach, Mr Ahern, has said.
Speaking at the weekend, he said he thought "the lesson of 1998 hopefully will be that people have the right to march but must also communicate with those people who they are asking to go into their areas. Where there is dialogue there are solutions".
He was speaking after a Requiem Mass at the Pro-Cathedral in Dublin for the three Quinn children murdered in Ballymoney, Co Antrim, eight days ago.
"Nobody can deny the burning of the house that led to the three Quinn boys dying shocked people back into their senses. But there is another terrible reality about the Troubles in the North that these things move on and they don't resolve the issues. "That is why we must use these periods to get people to understand what is the central issue, and that is they must speak to each other," said Mr Ahern, who attended the Mass with his partner, Ms Celia Larkin.
The President, Mrs McAleese, was represented by Comdt Dermot O'Connor. Also in the congregation were the British Ambassador, Ms Veronica Sutherland; the Lord Mayor of Dublin, Mr Joe Doyle; and the Minister of State at the Department of Justice, Equality and Law Reform, Ms Mary Wallace. Bishop Jim Moriarty, auxiliary bishop of Dublin, who was the principal celebrant, said the deaths "remind us of how much more remains to be done. The Christian message calls us forward to move out from behind our barricades of prejudice and hatred".
More than 500 people attended the Mass, including many children and members of peace and justice groups from North and South. Representatives from the Dublin-Monaghan Group, and the Meath Peace Group and Peace '93 read out prayers.
Ms Pat Campbell of the Belfast-based Women Together For Peace group, whose youngest son was murdered by the UFF in January 1992, told the congregation she hoped the Quinn family would be the last to suffer from the conflict. "We hope the terrible lesson learned from the last week will encourage people on all sides to try and find a way to live together in harmony and trust for the good of all mankind."