Francis, who was elected on March 13, arrived by helicopter at the papal summer residence at Castel Gandolfo for a meeting and lunch with Benedict, who has been living here since he abdicated on Feb. 28.
Vatican spokesman Father Federico Lombardi said Benedict and Francis embraced when the helicopter which brought Francis from Rome landed at the residence.
He added that Benedict's health was normal for a man of his age.
The pontiff and Benedict later prayed together in a chapel and held 45 minutes of private talks before starting a lunch, where they were joined by their two personal secretaries. Lombardi said the atmosphere was "family-like".
When they went to pray in the chapel, Benedict offered the place of honour, a kneeler before the altar, to Francis, who declined, saying, "We are brothers, we pray together." The two then prayed together from the same pew, Lombardi said.
Benedict, who became the first pope in 600 years to resign instead of ruling for life, is temporarily living in the residence in the Alban Hills.
He will move back to the Vatican after the restoration of a convent where he is expected to live for the rest of his life.
Shortly before his resignation, Benedict, now 85 and in failing health, said he would be "withdrawing into prayer" and would live out his remaining days "hidden from the world".
In February, on the last day of his nearly eight years as leader of the Catholic Church, Benedict pledged his unconditional obedience to whoever would succeed him.
The conclave of cardinals who elected Francis began on March 12 and chose Francis the next day.
While
the Vatican was not expected to give any information on what the two
discussed, it was likely that the conversation included problems of
Vatican administration.
LEAKS SCANDAL
Before
he resigned, Benedict left a secret report for Francis on the so-called
"Vatileaks" scandal in which sensitive papal documents were stolen from
the pope's desk and leaked to the media by his butler.
Last
year, the butler, Paolo Gabriele, was arrested and sentenced by a
Vatican court to 18 months in prison but Benedict pardoned him and he
was freed last Christmas.
The presence
of a reigning pope and a pope emeritus is new for the Church in the
modern era, but experts say it should not cause difficulties unless
Benedict tries to influence Francis's decisions, something he has
promised not to do.
Some Church scholars
worry that in the event that Francis undoes some of Benedict's policies
while he is still alive, the former pope could become a lightning rod
for conservatives and polarise the Church.
"Benedict
XVI could turn into a shadow pope who has stepped down but can still
exert indirect influence," Hans Kung, a dissident Swiss theologian who
has clashed with Benedict in the past, told a German magazine.
Benedict
now wears a simple white cassock without a cape, while Francis wears a
white cassock with a short cape, the traditional garb for a pope.