At a Mass in front of some 200,000 people in the eastern city of Santiago, he called for a "renewed society".
The Pontiff was welcomed by President Raul Castro who said the country enjoyed good relations with the Church.
His visit marks the 400th anniversary of Cuba's patron saint, the Virgin of Charity of El Cobre.
The icon - also known as the Mambisa Virgin - was found floating in a bay in 1612 by fishermen and was revered by Cuba's independence heroes.
"Devotion to the Virgin Mambisa has sustained the faith and inspired the defence and promotion of all that gives dignity to the human condition and fundamental rights," the Pope said on his arrival in the country, where Roman Catholics now account for 10% of the population.
"I carry in my heart the just aspirations and legitimate desires of all Cubans, wherever they may be, their sufferings and their joys, their concerns and their noblest desires," he said.
He added that he was convinced that the country "at this moment of particular importance in its history" was "looking to the future" and "striving to renew and broaden its horizons".
President Castro was seated in the front row of the Mass in Cuba's second largest city as believers sang hymns and prayed in Santiago's Revolution Square.
The Pope appealed to the audience to reinvigorate their faith "that you may strive to build a renewed and open society, a better society, one more worthy of humanity".
Before the Mass, one man was arrested after shouting: "Down with communism". Others in the audience booed him for spoiling the atmosphere and shouted: "Cuba, Cuba, Cuba".
BBC News - Pope Benedict calls for open society during Cuba visit (external - login to view)