The Vatican denied Monday that Pope Francis's Middle East trip has been driven by a political agenda, as Israel and Palestinians indulged in point-scoring over his impromptu gestures.

Francis "has no political agenda" and his unscheduled visits to the West Bank barrier Israel is building across the West Bank and to a memorial for Israeli civilians killed in militant attacks were "gestures" which "rounded out his official programme," Vatican spokesman Federico Lombardi said.

On Sunday, Francis made an unplanned stop by the separation barrier, climbing out of his open jeep to pray, his forehead and hand resting against the wall, in a powerful show of support for Palestinians.

His unscheduled stop Monday at national cemetery on Mount Herzl took place at the personal request of Israeli Prime Minister Benjamin Netanyahu to "balance" his trip, Lombardi said.

"I was not surprised to hear negative reactions in Israel over the pope's decision to stop and pray in front of the separation barrier," Lombardi said.

"The pope did not know about the (Israeli) memorial, and added it when it was possible."

The pope was winding up a packed trip which saw him issue a unique invitation to the Israeli and Palestinian presidents to pray with him at the Vatican to end their "increasingly unacceptable" conflict.

Palestinian president Mahmoud Abbas accepted the pope's visit saying he will go to the Vatican on June 6.

Israeli President Shimon Peres also welcomed the invitation to pray at the Vatican but his office did not specify a date.