The pontiff's landmark visit comes amid controvery over a deal last month to end Europe's refugee crisis by sending all irregular migrants who land in Greece back to Turkey.
At a refugee camp, where refugees knelt before the pope, one man cried "Father bless me" as the pontiff smiled and placed his hand on the man's head.
"This is a voyage marked by sadness, a sad voyage," the pope told reporters during the flight from Rome.
"And we are also going to a cemetery, the sea. So many people never arrived," he said.
More From This Section
An official from Greece's state refugee coordination agency said Francis, who has repeatedly spoken out about the plight of the migrants risking their lives to reach Europe, wanted to take back a small number of refugees from Lesbos.
The chosen refugees are expected to be from those who arrived on Lesbos before the EU-Turkey deportation deal took effect in March, the official told AFP, without specifying whether this would take place immediately after the pope's five-hour visit or at a later stage.
Lesbos has been the first port of call in the EU for hundreds of thousands of asylum-seekers fleeing war, poverty and persecution in the Middle East and Asia across the Aegean Sea from nearby Turkey in the past year.
The influx has sparked fierce disagreements between EU members and brought the bloc's system of open borders to the brink of collapse.
Lesbos has also become the focus of criticism of the EU's deal with Turkey to take back migrants who travel to the Greek islands on boats operated by people smugglers, in return for billions in EU cash.
Pope Francis, who was accompanied by Orthodox Patriarch Bartholomew and Archbishop Ieronymos, the head of the Church of Greece and Greek Prime Minister Alexis Tsipras, visited the Moria processing centre, which is currently housing around 3,000 people.