Couillard had a 45-second conversation with the pontiff at the Vatican and said it touched him very deeply.
"He had very moving words at the end and that surprised me," the premier said. "He said, 'I ask you to pray for me.' The Pope asking me to pray for him. I found that surprising and moving."
Couillard's one-on-one encounter with the leader of the Roman Catholic Church took place at the Pope's weekly general audience, which attracted tens of thousands of followers.
"I reminded him of the importance of the Catholic religion in our history and in our roots in Quebec," the premier said later. "He knew all about it. He knows Quebec very well."
Couillard also noted the enthusiasm that greeted the visit of Pope John Paul II to Quebec in 1984.
"Our relationship vis-a-vis the Catholic Church has changed over the years but one thing I've noticed is that it is still very important for more Quebecers than you think," said Couillard, whose four-day trip to Italy and France ends on Friday.
"Where did people go to get together in L'Isle-Verte and Lac-Megantic when tragedy struck? Church."
Couillard was referring to the train derailment in Lac-Megantic in July 2013 that killed 47 people as well as the fire at a seniors' home in L'Isle-Verte where 32 people died in January 2014.
It isn't clear when the Pope will reply to the invitation and Couillard gauged the chances of a papal visit at "50-50."
"Time will tell."
The offer follows a similar invitation from Montreal Mayor Denis Coderre last February.
Couillard also gave the Pope gifts from the Lac-Saint-Jean region: a pilgrim's staff and products from Trappist monks.
Later on Wednesday, the premier gave a speech to elected Italian officials.
He used the occasion to tell his audience about the main dates in Quebec's history and to speak about the influence of the Roman Catholic Church on generations of Quebecers.
Couillard will be in Paris on Thursday to meet French Prime Minister Manuel Valls and is also scheduled to attend a ceremony that day inducting Haitian-Quebecois writer Dany Laferriere into L'Academie francaise, France's council for the French language.
His main political foe, Parti Quebecois Leader Pierre Karl Peladeau, will also be at the Laferriere event as he visits Paris from Wednesday until Friday.
Couillard will return to Italy on Friday to discuss agricultural issues with United Nations officials.
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