Pope Francis has called for an end to the "increasingly unacceptable" Palestinian-Israeli conflict during a visit to the West Bank city of Bethlehem.

On the second leg of a three-day visit to the Middle East, Francis referred directly to the "state of Palestine", giving support for its bid for full statehood recognition in the face of a paralysed peace process.

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However, the Pope made clear that a negotiated accord was needed, calling on leaders from both sides to show the necessary courage to forge a deal.

"For the good of all, there is a need to intensify efforts and initiatives aimed at creating the conditions for a stable peace based on justice, on the recognition of the rights of every individual, and on mutual security," he said.

Later, in an unscheduled stop, he descended from his popemobile when it drove past the hulking grey concrete wall that Israel erected 10 years ago during a Palestinian uprising to divide Bethlehem from the adjacent Jerusalem. Israel says the wall is needed for security reasons.

The pontiff spent several minutes under the shadow of an Israeli watchtower and said a prayer.

"Free Palestine" was written in graffiti on the wall near where Francis paused.

Church officials say his tour of the region is focused on religious issues. However, the stark dividing lines of the Middle East conflict are impossible to ignore, and the Pope's every move has been scrutinised for meaning.

Abbas, Peres invited to the Vatican

Francis flew by helicopter to Bethlehem, becoming the first pontiff to travel directly to the West Bank rather than enter via Israel.

He later travelled to Israel from where he will return home on Monday, with some 8,000 police deployed in Jerusalem to guarantee his security.

The Pope's decision not to use a bullet-proof car meant Israeli security officials have cleared the roads and created numerous "sterile areas" ahead of his 24-hour stay in the city.

Standing alongside Palestinian president Mahmoud Abbas, Francis pointedly referred to him as "a man of peace and a peacemaker" before heading to Bethlehem's Manger Square, close to where Christians believe Jesus was born, to celebrate an open-air mass.

A mural behind the altar showed Jesus, who was a Jew, swaddled in a Palestinian keffiyeh, with his father, Joseph, also wearing the black and white headdress, made famous by the late Palestinian leader Yasser Arafat.

At the end of the mass, Francis invited Israeli president Shimon Peres and Mr Abbas to his home in the Vatican for a "heartfelt prayer" for peace.

"I offer my home in the Vatican as a place for this encounter of prayer," he said.

The leaders accepted the offer and are due to meet at the Vatican next month.

On Sunday evening, Francis prayed for Christian unity with Patriarch Bartholomew of Constantinople, spiritual leader of Orthodox Christians, in the Basilica of the Holy Sepulchre.

It was first time various branches of Christianity prayed together inside the centuries-old structure where Christians believe Jesus was buried and rose from the dead.

They usually are governed by strict rules of separation dating back to the Ottoman Empire.

The meeting was the main religious purpose of the trip, timed to commemorate the 50th anniversary of a historic meeting of Catholic and Orthodox leaders, whose Churches split in 1054.

Reuters