Bereaved families and survivors of a series of bombs have written an open letter to the Queen to mark her arrival in Ireland on the 37th anniversary of the atrocities.
A total of 34 men, women and children - including an unborn baby - were killed in the no-warning explosions in Dublin and Monaghan on 17th May 1974. It was the greatest loss of life in a single day of the Troubles.
Justice For The Forgotten has appealed to the monarch to urge Prime Minister David Cameron to open secret files which were withheld during an inquiry.
The campaign group believes the blasts were carried out by loyalist paramilitaries with British state collusion.
It wrote that while the Queen's visit is a sign of improving relations between the two islands and peoples, it wants the occasion marked by "a genuinely significant gesture of reconciliation".
Justice For The Forgotten said the sky did not fall in after Mr Cameron's historic apology for Bloody Sunday last June.
"So on this momentous occasion, our plea to Prime Minister Cameron is - pursue the truth with vigour, make us all stronger, open up the files," they wrote.
Victims of the bombings will be honoured at a wreath-laying ceremony at the Dublin memorial in Talbot Street on Tuesday morning, as the Queen begins her controversial visit.
Organisers have called on members of the public to attend the annual memorial for the dead, but asked that no flags, banners or emblems are displayed.
Margaret Urwin, spokeswoman for Justice For The Forgotten, said: "The extraordinary coincidence of the British monarch arriving on the actual anniversary of the worst atrocity in the history of the Troubles gives the British Government and British Prime Minister a wonderful opportunity to make a genuine, significant gesture of reconciliation."