Pope Francis invited Israeli President Shimon Peres and his Palestinian counterpart Mahmud Abbas on Sunday to his home in the Vatican for a "heartfelt prayer" for peace.

"I wish to invite you, president Mahmud Abbas, together with President Shimon Peres, to join me in heartfelt prayer to God for the gift of peace," he said at the end of an open-air mass in Manger Square in the West Bank town of Bethlehem.

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

"Building peace is difficult, but living without peace is a constant torment. The men and women of these lands, and of the entire world, all of them, ask us to bring before God their fervent hopes for peace."

As Francis entered the square to conduct the mass outside the Basilica of the Nativity, he was welcomed by 10,000 cheering pilgrims, who waved flags and sang hymns and carols as he drove up in a white open jeep.

Earlier, he urged an end to the "increasingly unacceptable" Israeli-Palestinian conflict, calling on leaders to show "courage" to achieve a peace based on a two-state solution.

"The time has come for everyone to find the courage... to forge a peace which rests on the acknowledgement by all of the right of two states to exist and to live in peace and security within internationally recognised borders," he said on meeting Abbas at his presidential palace.

Last month, US-led peace talks between Israeli and Palestinian negotiators collapsed in bitter recriminations. That ended a nine-month bid to reach a solution and left no political initiative on the horizon.