Pope Francis is visiting a detention camp on the Greek island of Lesbos, telling the migrants there that they "are not alone".
The Moria camp holds more than 3,000 people, some of whom may face deportation to Turkey.
Francis said his Greek trip was to witness "the worst humanitarian disaster since the Second World War".
Thousands are now stuck on Lesbos after last month's EU-Turkey deal to try to ease the flow of migrants.
The Vatican insists that the Pope's visit is purely humanitarian and religious in nature and should not be seen as a criticism of the deportations.
Why is Pope Francis going to Lesbos?
Short journey back from Lesbos to Turkey
Bewildered migrants await fate
Crisis explained in seven charts
Dozens of refugees lined up in the Moria camp to see the Pope, some holding banners asking for help.
Pope Francis met a group of young boys who had made the dangerous overseas journey alone. As he toured the camp, TV pictures showed one woman kneeling at his feet, delivering an emotional appeal.
A young girl handed him some artwork. The Pope said "Bravo, Bravo", before telling his staff: "Don't fold it. I want it on my desk."
In his speech, the Pope acknowledged "the great sacrifice" the people in the camp had made, saying he wanted to "draw the attention of the world to this grave humanitarian crisis".
Calling on the world to show "common humanity" over the crisis, he told the camp's residents: "Do not lose hope. The greatest gift we can offer to one another is love."
Pope Francis, Alexis Tsipras and Patriarch Bartholomew, Lesbos, 16 AprilImage copyrightReuters
Image caption
Pope Francis was met by PM Alexis Tsipras (C) and Archbishop of Athens Ieronimos II
A girl at the Moria camp, Lesbos, 16 AprilImage copyrightAFP
Image caption
A girl at the Moria camp prepares a poster for the Pope's visit
On his plane journey to Lesbos, the Pope told reporters: "This is a voyage marked by sadness... We will witness the worst humanitarian disaster since the Second World War.
"We will see so many people who are suffering, who are fleeing and do not know where to go. And we are also going to a cemetery, the sea. So many people never arrived."
The Pope was met at Lesbos Mytilene airport by Greek Prime Minister Alexis Tsipras, Patriarch Bartholomew, the spiritual head of the world's Orthodox Christians, and Archbishop of Athens Ieronimos II.
At the Moria camp, the Pope will also observe a minute's silence for those who have died making dangerous sea crossings in search of a better life.
Greece's ERT state television reported that Pope Francis had offered to take 10 refugees back to Italy with him. Vatican spokesman Rev Federico Lombardi said he could not comment.
In September, the Pope made space in the Vatican apartments for two refugee families, urging Catholics across Europe to play their part to resolve the crisis.
On the eve of the Lesbos visit, one Syrian attempted to kill himself at the camp after being told he would be deported back to Turkey but was prevented by police.
Migrants later demonstrated, demanding better treatment and to stay in Europe. They complain the camp is overcrowded and there is a lack of food.
Analysis - BBC diplomatic correspondent Caroline Hawley
Refugees and migrants line up inside Moria detention centre in Mytilene one day before the visit of Pope Francis on April 15, 2016Image copyrightAFP/Getty
This is a short, but highly symbolic visit designed to draw attention to what the Vatican has described as a difficult situation.
The Pope has repeatedly called for compassion to be shown to people fleeing terror, turmoil and hardship. He will be hoping his trip to Lesbos will stir Europe's conscience.
It comes as the EU's handling of the migrant crisis faces intense criticism from aid agencies and human rights groups. The Pope will meet refugees at a camp where more than 3,000 people are now effectively incarcerated in conditions aid workers say are deplorable.
He will then hold a ceremony to remember those who have died trying to reach Europe's shores. The Pope is coming with a strong moral message - but no solutions.
Some Syrians on Lesbos say they are terrified by the thought of returning to Turkey because of reports that hundreds of Syrians have been forcibly returned from Turkey to Syria.
Turkey has denied sending back any refugees against their will.
Migrant arrivals in Greece have fallen significantly this year, following the closure of borders and the announcement of the EU-Turkey deal.
In the week to 13 April, arrivals in Greece were 76% lower than the previous week, the International Organization for Migration said.
Pope Francis visited the Italian island of Lampedusa in 2013 to show similar support for migrants after dozens died trying to reach it.
GraphImage copyrightAFP
GraphImage copyrightAFP
Key points from EU-Turkey agreement
Returns: All "irregular migrants" crossing from Turkey into Greece from 20 March will be sent back. Each arrival will be individually assessed by the Greek authorities
One-for-one: For each Syrian returned to Turkey, a Syrian migrant will be resettled in the EU. Priority will be given to those who have not tried to illegally enter the EU and the number is capped at 72,000
Visa restrictions: Turkish nationals should have access to the Schengen passport-free zone by June. This will not apply to non-Schengen countries like Britain
Financial aid: The EU is to speed up the allocation of €3bn ($3.3 bn; £2.3 bn) in aid to Turkey to help migrants
Turkey EU membership: Both sides agreed to "re-energise" Turkey's bid to join the European bloc, with talks due by July
The Turkey-EU statement in full
Map locator
A note on terminology: The BBC uses the term migrant to refer to all people on the move who have yet to complete the legal process of claiming asylum. This group includes people fleeing war-torn countries such as Syria, who are likely to be granted refugee status, as well as people who are seeking jobs and better lives, who governments are likely to rule are economic migrants.
