The explosions in Ireland on 17 May 1974 killed 33 people - 25 in Dublin, eight in Monaghan - and injured nearly 200. The call for an inquiry has come from a campaign launched to coincide with the broadcast next Tuesday of a Yorkshire Television documentary.
The First Tuesday programme examines allegations that the explosions were planned for the same day as a vote in the Dail on anti-terrorist legislation allowing republican suspects to be jailed on the sole evidence of a garda officer that he believed someone to be an IRA member.
The vote had threatened to go against the government amid concern that the new law would be tantamount to internment. In the aftermath of the killings, the Bill was passed.
In Dublin, campaigners want a full investigation of allegations that a British Army intelligence officer helped to plan the attacks, believed to have been carried out by loyalists. The YTV programme reportedly claims to know the identity of an Army officer linked to the bombers.
No one has ever been charged over the bombings. The programme is expected to name four men who planted the bombs, and suggest that their identities are known to gardai.