Irish premier Bertie Ahern will ask Tony Blair to apologise for the wrongful conviction of the Guildford Four, the SDLP leader has claimed.
Gerry Conlon is campaigning for a public apology
Mark Durkan attended a meeting with Mr Ahern and Gerry Conlon, one of the Guildford four, who want a public apology from the British government.
Five people were killed when the IRA planted a bomb in the Horse and Groom pub in Guildford in October 1974.
The four jailed had their sentences quashed after doubts over evidence.
Gerry Conlon and his late father Giuseppe were both jailed over the bombing.
Mr Conlon and his mother Sarah met Mr Ahern in Dublin on Thursday after receiving a private acknowledgement that he and his family suffered a miscarriage of justice.
After the meeting Mr Durkan said Mr Ahern assured everyone that he would raise the issue with Mr Blair at a meeting next Tuesday.
"I believe Mr Blair is well-intentioned on the issue and will understand why the Conlon family needs closure for once and for all", Mr Durkan said.
Mr Conlon said Mr Blair was the first premier with the strength of character to issue a public apology.
His mother Sarah said: "A public apology would mean the world to me. Giuseppe went to jail as an IRA bomber and died in jail with people thinking he was an IRA bomber."
Mr Conlon's case was highlighted in the Oscar-nominated film In The Name Of The Father, starring Daniel Day-Lewis.
The Irish director of In The Name Of The Father, Jim Sheridan, also met Mr Conlon in Dublin to sign the family's petition.
Mr Conlon was one of four people initially detained after the Guildford attack, which claimed the lives of four soldiers and a civilian.
They and the Maguire Seven were later jailed in connection with the Guildford bomb and other bombings in Woolwich, south-east London.
Mr Conlon's father Giuseppe, who had a history of bronchial problem, died in prison in 1980 while serving his sentence.
A number of MPs, church leaders, journalists and legal figures raised concerns about the convictions.
In October 1989 the Court of Appeal quashed the sentences of the Guildford Four, and in June 1991 it overturned the sentences on the Maguire Seven.