"I sent heartfelt greetings to dear Mulsim immigrants who, this evening, will begin the Ramadan fast, and wish them them abundant spiritual rewards," Francis said in a homily as he held mass on the tiny Italian island.
"The Church is close to you in your search for a better lives for yourselves and your families," Francis stated.
During his visit to Lampedusa - his first outside Rome as pontiff - Francis said he had come to the island to "awaken consciences".
Some 15,000 people attended the open-air mass, held at Lampedusa's sports ground.
Lampedusa is the main European arrival point for migrants from North Africa. Thousands of migrants arrive on the island each year by boat and hundreds each week during the summer months as sea conditions improve.
Many thousands of migrants have drowned or died of dehydration during the dangerous journey across the southern Mediterranean, often crammed into unsafe people-smugglers' boats.
"When I heard a few weeks ago that more immigrants had drowned, the news was like a thorn piercing my heart," said Francis.
He was referring to an incident in mid-June when at least 10 migrants drowned off Malta when 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," Francis said.
"We have lost our sense of fraternal responsibility, he stated.
"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."
Earlier, Francis was greeted as he arrived on Lampedusa by its mayor, Giusy Nicolini, by the archbishop of the Sicilian city of Agrigento, monsignor Francesco Montenegro, and by the island's parish priest don Stefano Nastasi.
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 perished.
Earlier on Monday, 165 migrants arrived on Lampedusa, including four women. Media reports did not state how many people were currently being held in Lampedusa's immigration centre, which has suffered from chronic overcrowding.