Though security was stepped up around Jerusalem's holy sites, some Israelis gathered in the Old City's Jewish Quarter, where they tried - mostly without success - to catch a glimpse of the USA president.
He said earlier "there's a great feeling for peace throughout the Middle East", and suggested a potential warming by other countries toward Israel could be one "benefit" to the long-running tensions over Iran.
Abbas said he was keen to "keep the door open to dialogue with our Israeli neighbours".
He's urged Netanyahu to limit settlement construction and has also decided not to immediately move the USA embassy, a senior White House official said this month. There was no immediate claim of responsibility.
Trump's visit to the site sparked some controversy during the planning. Wednesday he is scheduled to visit Pope Francis in Vatican City.
Trump pushes for Mideast peace, but avoids thorny details
The president will be making five-stops-his next stop Israel, he's expected to meet with religious leaders and not politicians. To say that we do is to throw a terrible message to the rest of the world-and to make a mockery of principles and of realism.
Trump's visit to Jerusalem has been laden with religious symbolism.
U.S. Secretary of State Rex Tillerson would not say that the Western Wall is part of Israel when asked about by a reporter during the presidential flight from Saudi Arabia to Israel.
Trump prayed at the wall and placed a note between its bricks - a local tradition - while his daughter prayed in a separate section for women. A spokesman from the Israeli Ministry of Foreign Affairs denied any Israeli involvement in the matter, suggesting that it might have been a US security issue.
Under tight security and led by the traditional kawas honor guard announcing the way with the thumping of their ornamental staffs, the president made his way by foot through the Old City's alleyways to the Church of the Holy Sepulcher.
The White House struggled to answer the question.
Donald Trump denied Melania's hand - again
President Donald Trump has arrived in Bethlehem for a meeting with Palestinian President Mahmoud Abbas (mahk-MOOD' ah-BAHS'). Israel built the barrier a decade ago, saying it was a defense against Palestinian militants who carried out deadly attacks.
Israel has sought to downplay the concerns, saying security ties with the United States will continue to be strong.
After his comments at the airport, Trump shook hands and heard from various Israeli government members.
Trump is accused of disclosing the information during an Oval Office session with the Russian foreign minister and the Russian ambassador to the United States on May 10.
Along with the rest of her family, when U.S. President Donald Trump accompanied him Monday during his historic visit to the Western Wall in the Old City of Jerusalem, Ivanka Yael Trump Kushner was there as well.
"You have another story wrong", he said.
Senate Intelligence Committee issues two new Flynn subpoenas
The former Federal Bureau of Investigation head has agreed to testify before the Senate intelligence committee after Memorial Day. He previously had offered to testify to Congress in exchange for immunity from prosecution, a request lawmakers spurned.
Netanyahu then said "intelligence cooperation is terrific". But Trump's offhand remark was another stark reminder that his troubles at home, including the investigation of his campaign's ties to Russian Federation and his firing of FBI Director James Comey, have followed him across the ocean. They include easing travel between the West Bank and Jordan, developing two new industrial zones and increasing the number of building permits issued to Palestinians in parts of the West Bank where Jewish settlements are located near Arab communities. He also spoke about the "rare opportunity" to bring peace, stability and "future harmony" in the region. "It won't be simple". He is certain he will come here again, perhaps many times.
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