The prime minister also gave the Pope a set of books known as the Jesuit Relations, which Trudeau called "an essential tool for historians to understand the early years and stories of Jesuit missionaries documenting the origins of Canada".
"I told him about how important it is for Canadians that we move forward on real reconciliation with Indigenous peoples and highlighted how he could help by issuing an apology", Mr. Trudeau told reporters on Monday.
Canada's Truth and Reconciliation Commission has called for a papal apology, as part of the healing process for survivors.
Smith said any apology made by the pope would be best in person.
Canadian Prime Minister Justin Trudeau met with Pope Francis on Monday and asked him to apologize for the Catholic Church's role in the residential school system that abused indigenous children for more than a century.More news: President Trump wraps Mideast trip after Bethlehem, Jerusalem meetings
Canadian bishops have said the pope might visit next year.
The Vatican meeting, Trudeau said, was an opportunity to have "a deeply personal and wide-ranging, thoughtful conversation with the leader of my own faith".
Justin Trudeau, a Catholic, arrived in the Vatican this morning and met the Pope inside the Vatican's apostolic palace where the pair had a 36-minute private discussion.
For over a century, the schools were government-funded but many were administered by Christian Churches, the majority by Roman Catholics.
Absent from Trudeau's agenda for the audience were any topics related to life-issues, particularly that of euthanasia. The Canadian Supreme Court ruled unanimously in 2015 that people who are "grievously and irremediably ill" have a right to medical assistance in dying.More news: Kulbhushan Jadhav has been killed by Pakistan ?
But what really has the Internet riled up is The Pope's unenthusiastic expression when posing for a photo with Trudeau and his wife Sophie Gregoire - appropriately dubbed "Resting Pope Face".
Pope Francis, appreciating the gift, told the prime minister "it was a custom of the Jesuits" to compile such dictionaries when they began missions in new lands.
The Pope gave Trudeau a gold medal, an autographed copy of his message for World Peace Day and papal letters on family, evangelism and the environment. It also references the scripture passage from Matthew 5:7, "Blessed are the merciful, for they will be shown mercy".
Trudeau travelled to central Italy from Sicily after attending the G7 summit in Taormina on Friday and Saturday.
Canada's Truth and Reconciliation Commission said in a 2015 report that the practice, which kept children from the First Nations, Inuit and Métis peoples far from their parents, amounted to "cultural genocide".More news: WBBSE 10th result 2017: West Bengal Madhyamik class 10 results 2017 declared
"Pope Francis has a lot of influence on world thinking and is a very, very popular pope", Bellegarde said.