The Irish government is setting up a commission of inquiry into the Dublin and Monaghan bombings in 1974, in which 33 people and an unborn child died.
Nobody has been convicted of the 1974 bomb attacks
The commission is due to investigate the Garda's handling of the investigation, and the fact that key documents have gone missing.
But relatives of the victims criticised the move and demanded a full public inquiry rather than a private one.
They are calling on Dublin to press the UK to launch a joint inquiry.
The Justice for the Forgotten Group, representing the survivors of the bomb attacks, are unhappy with the Irish government's decision not to pursue a public inquiry into those events.
They say Irish Prime Minister Bertie Ahern has gone back on previous commitments to set up a public inquiry to investigate possible collusions between loyalist paramilitaries and British authorities in masterminding the attack.
Many of them believe that the Ulster Volunteer Force, who admitted their responsibility ten years ago, were helped by British intelligence.
"We have absolutely no confidence going into another private inquiry," said Margaret Urwin, the secretary of the relatives' group.
"We are very, very upset, we didn't expect this at all.
"Why does the Irish Government persist in hiding the truth of the Dublin and Monaghan bombings?
"Why does it continuously fail to set up a public inquiry when it has the power to do so?"
The group alleges British intelligence was aiming to warn the Irish government not to interfere in Northern Ireland's affairs.
The Irish government's announcement follows the conclusions of a parliamentary committee which studied a report by Mr Justice Barron into the bombings.
The report, presented to the Irish government in December and later made public, criticised the Irish government of the early 1970s and the original inquiry by the Garda.
It did not rule out the involvement of individual members of the Northern Ireland security forces, but found no evidence of collusion.
It said the group behind the attacks in Dublin could have carried them out without any help from the security forces.
Twenty-six people died in Dublin and seven in Monaghan in four car bomb attacks on 17 May 1974, while Protestant workers were holding a strike in Northern Ireland to bring down a power-sharing government set up under the Sunningdale Agreement.
More than 250 were injured in the attacks.