The first Vatican meeting between the leader of the world's Catholics and the highest authority in Sunni Islam marks the culmination of a significant improvement in relations between the two faiths since Francis took office in 2013.
"Our meeting is the message," Francis said in a brief comment at the start of his meeting with Sheikh Ahmed al-Tayeb, Vatican officials told a small pool of reporters covering the event.
In a statement on the trip, Al-Azhar, an institution that also comprises a prestigious seat of learning, said Tayeb had accepted Francis's invitation in order to "explore efforts to spread peace and co-existence."
Tayeb's decision to fly to Rome, unexpectedly announced last week, followed the easing of serious tensions that marked the reign of Francis's predecessor, Benedict XVI.
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Ties were badly soured when the now-retired Benedict made a September 2006 speech in which he was perceived to have linked Islam to violence, sparking deadly protests in several countries and reprisal attacks on Christians.
Pope John-Paul II met the then-grand imam of Al-Azhar in Cairo in 2000, a year before the September 11 attacks on New York transformed relations between the West and the Islamic world.
Vatican spokesman Federico Lombardi said in a statement that the pope and the imam had "mainly addressed the common challenges faced by the authorities and faithful of the major religions of the world."
These included working together for world peace, rejecting violence and terrorism, and the situation and protection of Christians against a backdrop of conflict and terrorism in the Middle East."
The pope presented the imam with a copy of his recent encyclical, Laudato Si', a letter to the faithful in which he urges the world to wake up to the threat posed by climate change and also calls for a rebalancing of the economic relationship between the industrialised and developing worlds.
"If it were not for these good positions the meeting would not be happening," imam's deputy Abbas Shuman said.