Francis' address to families and symbolically potent flight to the United States underscore two of the big themes of his Cuba pilgrimage: encouraging reconciliation within families and between the US and Cuba.
He worked behind the scenes as mediator in 18 months of secret talks on re-establishing diplomatic relations between the two nations.
On his arrival in Cuba, the pope described the success of the negotiations as an example of peacemaking for the entire world.
Beyond its importance to the pope, the state of the family has been a longtime concern for the Roman Catholic Church in Cuba. Economic deprivation and successive waves of emigration have left many families broken and divided, and the church has focused intensely in recent years on trying to encourage traditional values like hard work, respect and fidelity that many Cubans worry have been lost over the years.
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Those concerns about moral degradation are widespread among Cubans regardless of how religious they are.
The foot-tall wooden statue is kept in an ivory-colored church with soaring red domes nestled in the shadow of the Sierra Maestra mountains in the small community of Cobre just outside Santiago.
One corner of the church where Francis celebrated Mass Tuesday Mass is dedicated to offerings left for the Virgin, including votives and thousands of handwritten notes.
"She means so much," said Juana Isabel Gonzalez Huart, a retired state worker. "She's the mother who protects us."
He told the crowd of how Jesus picked a lowly and despised tax collector, Matthew, and instructed him without casting judgment to follow him. That act of mercy changed Matthew forever.
Francis told the Cubans that they, too, should allow themselves "to slowly overcome our preconceptions and our reluctance to think that others, much less ourselves, can change.