The 1974 bombings killed 34 men, women and children and injured another 300 when loyalist paramilitaries brought death across the border.
The Queen will arrive in Dublin on the 37th anniversary of the bombings on Tuesday amid calls from survivors and victim support groups to open top secret British files on the events of 1974.
Ireland’s parliament is also to debate a Sinn Fein motion on Tuesday which repeats a 2008 all-party call on the British government to release all files on the Dublin and Monaghan bombings.
The Justice for the Forgotten group – which represents survivors and families of those affected by the Troubles – has already written to the Queen on the subject.
In their letter to Queen Elizabeth, the group has called on British Prime Minister David Cameron to ‘pursue the truth with vigor - make us all stronger - open up the files’.
The 2003 Barron report into the bombings ruled that they were carried out by loyalist paramilitaries but said there were grounds for suspicion that the bombers were aided by security forces in the North.
An Irish parliament committee report also suggested collusion between the bombers and British security forces on the ground in Northern Ireland.
In its letter, the Justice for the Forgotten group tells the Queen that her visit is a sign of improving relations between Ireland and England.
It adds: “We are appealing, through you, to your Prime Minister David Cameron, to mark the occasion of this historic visit by a genuinely significant gesture of reconciliation.”
The group has advertised its letter in the national press, and asked for donations from members of the Irish parliament to pay for it.