"I sent heartfelt greetings to dear Muslim immigrants who, this evening (Monday), will begin the Ramadan fast, and wish them abundant spiritual rewards," Pope Francis said as he held mass on the tiny Italian island of Lampedusa.
"The Church is close to you in your search for better lives for yourselves and your families," Francis said.
During his visit to Lampedusa, his first outside Rome as pontiff, Francis said he came to the island to "awaken consciences".
Around 15,000 people attended the mass.
Lampedusa is the main European arrival point for migrants from North Africa. Thousands of migrants arrive on the island each year by boat during the summer months.
Several thousands of migrants have drowned or died of dehydration during the dangerous journey across the southern Mediterranean, often crammed into unsafe boats.
"When I heard a few weeks ago that more immigrants had drowned, the news was like a thorn piercing my heart," Francis said.
He was referring to an incident in June when at least 10 migrants drowned off Malta after a Tunisian fishing boat allegedly refused to rescue them.
"I felt I must come to Lampedusa to pray that such a tragedy doesn't happen again," the Pope said.
"We have lost our sense of fraternal responsibility," he said.
"The culture of affluence has made us insensitive to the needs of others. We are living in a soap bubble, a situation that makes us indifferent to others, indeed which has led to the globalisation of indifference."
The pontiff met around 50 migrants at Lampedusa's port and was then taken on a short boat ride to a nearby bay, where he cast a wreath into the sea in memory of migrants who had died.
Earlier Monday, as many as 165 migrants including four women arrived in Lampedusa. Media reports say Lampedusa's migration centre is suffering from chronic overcrowding.
The Delhi High Court Monday issued notice to the CBI and two accused who were acquitted of murder charges in a 1984 anti-Sikh riots case.