The deal with Turkey includes a provision under which migrants arriving in Greece can be swiftly deported back to Turkey. Since the deal took effect last month, the number of migrants arriving in Lesbos has dropped sharply (even as the numbers arriving in Italy are steadily rising). Critics say the agreement has trampled on the civil rights of refugees fleeing war and betrayed the ideals of the European Union.

At the migrants camp, Ecumenical Patriarch Bartholomew, the spiritual leader of the world’s Eastern Orthodox Christians, reminded Europeans and their leaders that Christians and others are judged on how they treat the powerless. “The world will be judged by the way it has treated you,” Bartholomew told the refugees. “And we will all be accountable for the way we respond to the crisis and conflict in the regions that you come from. The Mediterranean Sea should not be a tomb.”

Thousands of migrants have drowned in the Mediterranean, including a young child whose limp body washed ashore last year on the Turkish coast. A photograph of the child became a searing icon of the refugee crisis. “I hope that we never see children washing up on the shores of the Aegean Sea,” said Archbishop Ieronymos II, the leader of the Greek Orthodox Church, who called for a greater response by the United Nations. “I hope to soon see them there, untroubled, enjoying life.”

At the Moria center, Francis slowly walked down a line of migrants, many of them Muslims, greeting people as some waved handwritten signs with slogans like “Freedom of Movement.” Others propped their children above their shoulders or held out smartphones to photograph the pope.

Inside a large white tent, Francis greeted a woman in a head scarf as she cradled her baby, as well as other refugee families. A small boy stepped forward and handed him a picture drawn with crayons. An Iraqi mother asked Francis to help her find medical care for her child’s bone cancer. At one point, a man began wailing as Francis placed his hands on the man’s head. “Please, Father, bless me!” the man shouted. “Please, Father, bless me!”

Francis and the other religious leaders offered special praise on Saturday for ordinary Greeks who have welcomed refugees, taken some into their homes or provided food and clothing, even as they endure hardship amid the country’s long-running financial crisis. Mr. Tsipras and other Greek leaders have called on the European Union to provide more help to the country as it has borne the brunt of the migrant crisis.

Across Europe, the mood has soured in recent months, as many countries have closed or restricted their borders amid mounting public anxiety over the chaotic influx of more than a million refugees last year. The recent terrorist attacks in Paris and Brussels have also darkened public attitudes and stirred anti-migrant sentiment in some areas, even as many refugees say they are trying to escape extremist violence. Far-right, anti-immigrant parties have seized on the crisis to make gains, most recently in regional elections in Germany.