The Irish Government is facing fresh pressure to appeal against a European court decision that found the so-called Hooded Men did not suffer torture.
Speaking before putting a motion to the Seanad, Sinn Fein senator Niall O Donnghaile said he wanted the government to "see the case through" and challenge the decision, made by the European Court of Human Rights (ECHR) in March.
Mr O Donnghaile said: "It's about vindication for these men and what they went through but also the people who continue to suffer torture around the world."
One of the men, Liam Shannon (70), who was at Leinster House in Dublin yesterday to see the motion put forward, said the decision was "massively" important to the men.
He said: "We've been going at this for 47 and a half years, trying to get justice, just to get the truth.
"We are going to continue, it doesn't matter how it goes, we are going to continue and we will get the truth in the end."
He added: "We can only hope that the Irish Government will fulfil its obligation and continue what they started and finish this off."
The 14 Catholics who were detained indefinitely without trial in 1971, said they were subjected to a number of torture methods.
These included five techniques: hooding, stress positions, white noise, sleep deprivation and deprivation of food and water, along with beatings and death threats.
The men were hooded and flown by helicopter to a secret location, later revealed to be a British Army camp at Ballykelly, outside Londonderry.
In March, ECHR dismissed Ireland's request to find the men suffered torture by six votes to one and said there was "no justification" for revising a 1978 ruling.
The court said new evidence had not demonstrated the existence of facts that were not known to the court at the time or which could have had a decisive influence on the original judgment.
The Irish Government first took a human rights case against Britain over the alleged torture in 1971.
The European Commission of Human Rights ruled that the mistreatment of the men was torture, but in 1978 the European Court of Human Rights held that the men suffered inhumane and degrading treatment that was not torture.