"One image from the pope's visit has already become history," admitted Israeli daily Yediot Aharonot, saying the picture of the pope's impromptu stop to rest his hand and forehead on the wall "immediately became a Palestinian PR achievement."
Hanan Ashrawi, a senior member of the Palestine Liberation Organisation (PLO), said "the Palestinians were touched" by his gesture and the pope was also "clearly moved by the experience."
Francis's decision to fly directly from Jordan to Bethlehem rather than starting his trip in Israel -- which ruffled feathers in the Jewish state -- was seen as "active recognition of the state of Palestine," she said.
When he met children in the Dheishe refugee camp, the 77-year-old was presented with a key, symbolising Palestinians' yearning to return, as well as a mocked-up refugee card bearing the name of Jesus.
And during the open-air mass he celebrated in Bethlehem, he stood in front of a vast mural of a nativity scene showing the infant Jesus swaddled in a traditional Palestinian keffiyeh scarf.
The decisive morale boost for the Palestinians was not well received in Israel.
"Obviously the Palestinians laid well prepared traps for the pope which were used as part of their instrumentalisation of this visit for propaganda purposes," foreign ministry spokesman Yigal Palmor told AFP.
Ever aware of the PR value of such an image, Israel quickly moved to counter the blow with Israeli Prime Minister Benjamin Netanyahu reportedly making a personal request for Francis to visit a national memorial for victims of militant attacks on Mt Herzl.
There, as Francis touched the marble plaques bearing the names of the victims, Netanyahu explained Israel's rational for the barrier.
"We don't teach our children to plant bombs. We teach them peace. But we have to build a wall against those who teach the other side," he said, later adding: "After it was set up, the terror stopped."
Politics through religion?
Religious watcher John Allen, who writes for the Boston Globe, said the stop was undoubtedly "an iconic visual that will resonate long after Francis is back in Rome".
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The Vatican rushed to limit the fallout, with spokesman Federico Lombardi insisting Francis's unscheduled stop at the graffitied wall was "a personal decision" and not a politically-motivated act.
Lombardi also said the pope had hoped his emotional embrace at the Western Wall with two old friends travelling with him -- Rabbi Abraham Skorka and Islamic studies professor Omar Abboud -- would help mollify both sides.
"He managed to be political by being religious -- exclusively religious," said Pascal Gollnisch, head of the French Catholic NGO Oeuvre d'Orient.
Vatican expert Andrea Tornielli, who writes for La Stampa's Vatican Insider and who knows the pontiff personally, rebuffed talk of point scoring, saying the pope "was not exploited by either the Israelis or the Palestinians."
Spontaneous by nature, Francis empathised with "the suffering of everyone, of all parties" through gestures which showed his "capacity to physically convey his support," he told AFP.
'A royal flush'
But Israeli commentators said both sides had crossed red lines in the bid to own the visit of the head of the world's 1.2 billion Catholics.
"In the pope's visit to the Middle East, both hosting sides crossed all the boundaries. Both the Palestinians and the Israelis deviated from the original plan and waged a war of tricks and shticks (gimmicks) at the expense of the leader of the Catholics," wrote Eitan Haber in Yediot Aharonot.
"Many in the world, not just Catholics, are not pleased with the games that were played using the pope."
Writing in the left-leaning Haaretz, columnist Matthew Kalman said the immediacy of the wall and the message of suffering it conveyed clearly gave the Palestinians the upper hand.
"Israelis take their visitors to Yad Vashem (Holocaust museum) to recall Jewish suffering a half century ago, more than one thousand miles away.
"But Palestinians take their visitors to the wall, the 30-foot-high, ugly, towering proof of Israeli-inflicted suffering, right here, right now," he wrote.
"In the complex game of Papal propaganda poker, that's a Royal Flush for the Palestinians."