Speaking on the BBC Inside Politics programme, Mr Robinson said the Taoiseach Enda Kenny should apologise for the role previous Irish governments played in arming and encouraging the IRA.
Recently Mr Kenny told relatives of the Kingsmills massacre, in which ten textile workers were murdered on their way home from the County Armagh textile factory in 1976,that he could not apologise for the IRA.
Mr Robinson, who is an MLA for East Belfast, accepted that Mr Kenny could not apologise for the IRA.
“Nobody would be apologising for the IRA, other than those in the Republican movement. What he does need to apologise for, is the role of the Irish government. There is a clear connection between what the IRA did in its infancy and the government of the Irish Republic.”
He added, “I think the Irish Republic would do well to look at its role and recognise that it was not the way it should have behaved in those days and apologise for it because massive death and destruction followed.”
It has now emerged that Mr Robinson, who is leader of the Democratic Unionise Party, has tabled a motion this week for the Stormont Executive seeking an apology.
The motion says it, “welcomes the improved relations with the Republic of Ireland.” However it adds that it, “believes that relations would improve further,” with an apology from the current Irish government for, “the role played by the Irish government of the day in the emergence of the Provisional IRA and the roles of past governments regarding the pursuit of terrorists.”