* Raul Castro says Church, Cuba agree on many things
* Pope, Fidel Castro discuss world, joke about age
* Pope calls on Cuba to give Church bigger role
(Updates with pope departure, adds quotes, details)
By Philip Pullella and Jeff Franks
HAVANA, March 28 (Reuters) - Pope Benedict called for an end
to the U.S. trade embargo against Cuba and met with
revolutionary icon Fidel Castro on Wednesday as he ended a trip
in which he urged the communist island to change.
He also spoke at a public Mass in Havana's sprawling
Revolution Square where the Vatican said 300,000 people gathered
to hear the 84-year-old pontiff.
In a trip laced with calls for change in Cuba, his last
message was aimed at the United States, its longtime ideological
foe, which for 50 years has imposed a trade embargo trying to
topple the Caribbean island's communist government.
Speaking in a departure ceremony at a rainy Havana airport,
Benedict said Cuba could build "a society of broad vision,
renewed and reconciled," but it was more difficult "when
restrictive economic measures, imposed from outside the country,
unfairly burden its people."
"The present hour urgently demands that in personal,
national and international co-existence we reject immovable
positions and unilateral viewpoints," the German pope, dressed
in white vestments, said in his soft voice and heavily accented
Spanish.
Beginning at his arrival in eastern Santiago de Cuba on
Monday, Benedict sprinkled his speeches with thinly-veiled
references to Cuban dissidents, political prisoners, Cuban
exiles and the need for the Caribbean island to push ahead with
its economic reforms.
The pontiff rode in his Popemobile on the way to the airport
and was bid farewell by streets lined with Cubans waving flags
and cheering him.
President Raul Castro, who attended the pope's Masses in
Santiago on Monday and in Havana on Wednesday, saw off the
pontiff, who is frail and moves slowly, before he boarded his
jet for Rome and flew into stormy skies.
The two men clasped hands and Raul Castro dipped his head
briefly in a show of reverence that he had made at their other
meetings. Both he and his older brother were educated by
Jesuits, the worldwide Catholic order.
MUTUAL UNDERSTANDING
"Your visit has taken place in an atmosphere of mutual
understanding," President Castro said. "Your holiness, we have
found many and deep agreements, although it's natural that we
don't think the same on all issues."
Under 49 years of rule by Fidel Castro, the Roman Catholic
Church lost its schools, hospitals, access to media and its
prominent role in Cuban society.
But Raul Castro, who succeeded his ailing brother four years
ago, has improved relations with the Church and is using it as
interlocutor on issues such as political prisoners and
dissidents as he undertakes potentially disruptive reforms to
the country's struggling Soviet-style economy.
He is encouraging more private enterprise to offset plans to
cut 1 million jobs from government payrolls, which is 20 percent
of the country's labor force of 5.2 million.
But while Benedict is urging Cuba to make deeper changes,
the government sees its reforms as a way of strengthening
communist rule, not weakening it.
The pope mentioned several times during his visit that he
was happy relations had improved, but also said they needed to
get better so the Church could help buffer against "trauma" or
social upheaval.
"This must continue forwards, and I wish to encourage the
country's government authorities to strengthen what has already
been achieved and advance along this path," he said.
The Church, he added, "seeks to give witness by her
preaching and teaching, both in catechesis and in schools and
universities."
After the Mass, Fidel Castro, the president's older brother,
visited Benedict at the Vatican embassy where the two
octogenarian world leaders with widely divergent political views
chatted for 30 minutes in what a Vatican spokesman called a
"very cordial" atmosphere.
They discussed serious issues such as Church liturgy and the
state of the world, but also joked about their age -- Benedict
is 84. At one point, Fidel Castro asked a simple question - what
does a pope do?
"The pope told him of his ministry, his trips, and his
service to the Church," said spokesman Federico Lombardi
ARMED GUARDS.
Photographs showed the elder Castro and the pope shaking
hands and smiling, with Castro wearing a dark track suit and a
scarf around his neck that seemed out of place on a warm day.
Witnesses said the former comandante arrived in a green
Mercedes SUV with armed guards in a surrounding phalanx of black
Mercedes sedans.
Two assistants helped Fidel Castro, who has been in frail
health since 2006, out of the car, then up the steps of the
stately white embassy in Havana's Miramar district.
The friendly meeting contrasted with the beginning of
Benedict's visit when he sharply criticized the communist system
that Castro put in place after taking power in a 1959 revolution
and continues to defend as the last, best hope of mankind.
On the flight to Mexico beginning his Latin American trip on
Friday, the pope said communism had failed in Cuba and that the
country needs a new economic model.
In a possible dig at Marxism on Wednesday, Benedict said in
his Mass that some "wrongly interpret this search for the truth,
leading them to irrationality and fanaticism; they close
themselves in 'their truth,' and try to impose it on others."
He said the said the search for truth "always supposes the
exercise of authentic freedom."
The Church wants to get back some of the ground it lost
after the revolution, so the pope urged the government to let it
do more social work and play a bigger role in education.
Marino Murillo, a vice president in the Council of Ministers
and the country's economic reforms czar, made it clear that
change to Cuba's one-party political system is not in the works.
"In Cuba there won't be political reform," he said at a news
conference. "We are talking about the update of the Cuban
economic model to make our socialism sustainable."
(Additional reporting by Simon Gardner, Rosa Tania Valdes and
Nelson Acosta; Editing by David Adams and Kieran Murray)
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