Pope Francis has made a personal bid for peace by inviting the Israeli and Palestinian presidents to the Vatican to pray for an end to their “increasingly unacceptable” conflict.

And he came face-to-face on Sunday with daily Palestinian reality in Bethlehem, making an unscheduled stop by a towering separation barrier Israel is erecting across the West Bank to talk with families and refugees.

But as he arrived to begin the Israeli leg of his three-day visit to the Middle East, the 77-year-old pontiff expressed deep sadness over a deadly shooting attack in Brussels that left four people dead, two of them Israelis, calling for an end to anti-Semitism and intolerance.

As he clambered out of a Jordanian military helicopter at Tel Aviv airport, Israeli and Vatican flags snapped jauntily in the breeze as Francis was greeted on the red carpet by Israeli President Shimon Peres and other top officials.

Although Francis has said his three-day pilgrimage, which has already taken him to Jordan and the occupied West Bank, has “purely religious” motives, his every gesture was closely scrutinised with Israel and the Palestinians keen to score a few political points.

Earlier, he grabbed headlines in Bethlehem with an unscheduled stop by the West Bank barrier, hopping out of his jeep to spend a few minutes in prayer, resting his forehead against the graffitied concrete wall.

Dressed in his white cassock and flanked by anxious Palestinian security guards, he walked over to the eight-metre high barrier, which is topped by a guard tower.

He rested his hand and forehead on the “Free Palestine” daubed wall, and then paused several minutes in front of a scrawled appeal for his help: “Pope we need someone to speak about justice.”

It was a powerful show of support which was warmly welcomed by the Palestinians.

“It was an eloquent and clear message to the whole world, particularly to Israel, that we cannot reach peace while Israel continues to build racist separation walls between the Palestinian and Israeli peoples,” said Nimr Hammad, political adviser to Palestinian president Mahmud Abbas.

Israel say the vast barrier, which they began building in 2002, is crucial for its security. Palestinians see it as a land grab aimed at stealing land they want for a future state.

On arrival in Israel, Francis said he was “profoundly saddened” by the attack at the Jewish museum in Brussels, and he used his speech to issue a call for an end to anti-Semitism.

“Let us promote an education … where there will be no place for anti-Semitism in any of its forms or for expressions of hostility, discrimination or intolerance towards any individual or people,” he said.

Leaving Tel Aviv, Francis was flown to Jerusalem in a Black Hawk helicopter where he was met by a group of Jewish, Christian and Muslim schoolchildren, beaming widely as they handed him a basket of fruit and another basket of Holy Land earth.

Despite expectations he would steer clear of the thorny politics of the intractible Israeli-Palestinian conflict, the Argentine pontiff extended a personal invitation to Abbas and Israeli counterpart Peres to join him at his home in the Vatican for a “heartfelt prayer” for peace.

“Building peace is difficult but living without peace is a constant torment,” he said.