Pope Francis, who has taken over a Catholic Church beset by scandal, should watch the film, director Stephen Frears said.
"I'm very keen that the Pope should see it," he said.
Philomena debuted at the Venice film festival alongside James Franco's Child of God the chilling tale of a cave-dwelling necrophiliac, and Night Moves about three eco-warriors who plot to blow up a dam.
Asked why he had made a film about such a taboo subject, Franco said it had provided a way "for me to examine something that's pushed out of civilised society.
Philomena is based on The Lost Child of Philomena Lee, the 2009 book by Martin Sixsmith which prompted thousands of adopted Irish children and their mothers to come forward and tell their stories.
Philomena goes to America to look for her son with world-weary journalist Sixsmith, played by co-writer Steve Coogan, creating what Frears describes as "an odd-couple film, an extraordinary road trip".
"I really liked the British humour which contrasts with the religious issues," said Jacopo Mascholini, a 22-year-old student from Rome who attended the screening.
Put to work in a Catholic laundry after having a baby out of wedlock in 1952, Philomena loses her son to strangers and is prevented from finding him again, but does not lose her Catholic religion.
Philomena's uncomplicated faith is emphasised by the cynicism of Sixsmith, who lost his job as a British government spin doctor in 2002, beset by controversy over an email that allegedly said 11 September was a good day to bury bad news.
Sixsmith asks Philomena during the film why God gave people sexual desires if the church would then brand them sinful.
"Was it some weird game to relieve the boredom of being omnipotent?" he asks.
"The real Philomena's faith I found very affecting, but my heart is much more with the cynical journalist," Frears said.
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