"If you have been indifferent, take a risk -- you won't be disappointed. If following him seems difficult, don't be afraid, trust him, be confident that he is close to you," the pope said.
The leader of the world's 1.2 billion Catholics, formerly archbishop of Buenos Aires Jorge Bergoglio, also told thousands of worshippers at the grandiose mass not to "lose confidence."
"Do we feel weighed down by our sins? Do we think that we won't be able to cope? Let us not close our hearts," he said.
"Let us not lose confidence, let us never give up: there are no situations which God cannot change," he added.
The mass wrapped up a series of ceremonies leading up to Easter Sunday -- the holiest day in the Christian calendar, which commemorates the resurrection of Jesus Christ.
Tens of thousands of people are expected at mass on Sunday when the pope will also issue a special blessing from the same balcony of St Peter's Basilica where he appeared on the night of his momentous election earlier this month.
In only the second time in history, a 30-minute showing of the Holy Shroud -- which according to Catholic tradition wrapped the crucified body of Christ -- was broadcast live on Saturday afternoon by Italian public channel Rai Uno to mark the celebrations. The first time it was broadcast was in 1973.
"The face of the shroud communicates great peace," the pope said in a video-recorded message ahead of the exhibition. "It is as if he is saying: 'have confidence, do not lose hope, the power of God's love, the force of the resurrected, conquers all.'"
Giovanni Maria Vian, editor of the Vatican's official daily Osservatore Romano, said the new pope's energy during the Easter season helped explain the timing of his ageing predecessor Benedict XVI's shock resignation.
"It is in these crucial liturgical days that we have heard the strength of the voice of a pope who has come for the first time almost from 'the ends of the world' as he himself said," Vian wrote.
"In all his life as priest and bishop he has always shown a special concern for material and spiritual peripheries," he said, underlining the pope's Holy Week message of bringing the troubled Roman Catholic Church closer to the needy.
Francis marked Good Friday with a traditional torch-lit ceremony at the Colosseum in Rome, presiding over a re-enactment of Christ's last hours.
The pope prayed for Middle East peace and greater Christian-Muslim dialogue -- a theme he has already referred to in the first days of his reign.
On Holy Thursday, Francis washed the feet of 12 young prisoners including two Muslim inmates at a youth prison in the outskirts of Rome in an unprecedented new take on an ancient pre-Easter ritual.
Popes performing the ceremony -- which commemorates the gesture of humility believed to have been carried out by Jesus for his 12 disciples -- have usually washed the feet of priests.
Latin America's first pontiff has set a markedly different tone from his predecessor, with a more informal style that is unusual in the Vatican.
He was known in his Argentina for his humble lifestyle, his outreach in poor neighborhoods, and his strong social advocacy during his homeland's devastating economic crisis.
Vatican experts say he is yet to begin tackling the many problems assailing the Church, however, including reform of the scandal-ridden Vatican bureaucracy.
Analysts will keep a particularly close eye on Vatican appointments to key positions after Easter amid calls from inside the Church for an overhaul.
Another test will be how he handles the scandal of thousands of cases of child abuse by pedophile priests going back decades -- many of which were hushed up.
Benedict's eight-year regin was often overshadowed by the scandals, including an embarrassing leak of hundreds of confidential Vatican papers last week that revealed cloak-and-dagger intrigue.