A Plea For Peace, directed by David Naglieri and narrated by The Passion Of The Christ star Jim Caviezel, features interviews with Seamus Mallon, Martin Mansergh, Rev Harold Good, Lord David Alton and former IRA bomber Shane Paul O'Doherty.
O'Doherty's letter-bomb campaign caused explosions at the London Stock Exchange, the Bank of England, and a government building, injuring secretaries and security guards.
O'Doherty, who joined the IRA in Londonderry at 15, found religion while serving a life sentence, and famously wrote to his victims from prison, crediting the Catholic Church for sparking a major turning point in peace negotiations.
"When I first turned away from the IRA and apologised to my victims, I was not taken seriously, everyone thought I wanted early release.
"I was in prison in England when suddenly the Pope arrives in Ireland and speaks to these men, asking them to turn away from violence and make a new life. Suddenly I was taken seriously.
"Weeks after his visit, I had been visited by senior Labour MPs and Father Edward Daly.
"I was the first IRA man to publicly turn away from the IRA in 1977, and after the Pope's visit, scores of other prisoners left.
"To put the Pope's visit in context, 28 days before the visit, Mountbatten was killed along with 18 soldiers.
"I believe that was the closest Northern Ireland had ever come to civil war."
The film focuses on the Pope's famous appeal in Drogheda: "On my knees I beg you to turn away from the paths of violence and return to the ways of peace," in front of a quarter a million people, and argues this sowed the earliest seeds of peace.
Mr Naglieri said the film-makers discovered handwritten letters from Father Alec Reid to John Hume, which directly quoted the papal message.
"Through researching, at first we found a lot of cynicism - people said the violence continued for two decades after the visit, and superficially it didn't have much effect - but for us it was a lot of peeling the onion," he said.
"The thesis is not that the Good Friday Agreement wouldn't have happened if he didn't come, but we're tracing the ripple effects of the Pope's visit.
"For instance, Protestant leaders in the documentary say that speech was the break, where they first separated the Catholic Church from the IRA.
"However, the strongest case for the impact of the visit is the letters from Father Alec Reid.
"On May 19 1986 Father Alec Reid writes a seven-page letter to John Hume and references the speech in Drogheda twice, pointing to the part about dialogue being the way forward, and this ultimately sparks the secret meetings between John Hume and Gerry Adams, which lead to the peace process.
"The words germinated in the minds of peace makers, and without that happening Good Friday doesn't happen."
John Paul II In Ireland: A Plea For Peace will have a limited theatrical release with Omniplex cinemas in the Republic of Ireland and Northern Ireland in late September.
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