Mr. Trump was seen placing a note inside the wall as he visited the mens-only side - a tradition visitors can partake in by writing a prayer or request and placing it in one of the wall's cracks.
The White House insists that Trump did not divulge the source of his intelligence about potential terrorist threats emanating from Syria, but intelligence agencies worry that details of the plot could allow the Russians to identify where the information came from.
Asked if he agrees with the USA ambassador to the United Nations, Nikki Haley, who last week asserted during an interview that "We've always thought the Western Wall was part of Israel", Tillerson responded: "The wall is part of Jerusalem".
That page listed just "Jerusalem" for two other videos or remarks he made before meetings with Netanyahu and President Reuven Rivlin.
"We also have to be concerned about security issues", said Danon.More news: Trump arrives for talks with Palestinian leader in Bethlehem
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But when it comes to the Western Wall, real estate plays as large a role as religious faith. The global community does not recognise Israeli sovereignty over Jerusalem and maintain their embassies in Tel Aviv.
It is situated below the Al-Aqsa mosque compound, Islam's third-holiest site, referred to by Jews as the Temple Mount and considered their holiest. Security was tight, with the usually bustling Old City, where the Western Wall is located, essentially on lockdown and the plaza leading to the site cleared. His wife, Melania, daughter Ivanka and son- in-law Jared Kushner accompanied him.
Israeli police stand by the body of a Palestinian who was shot and killed after he attempted to stab an Israeli soldier at a checkpoint north of the West Bank city of Bethlehem, Monday, May 22, 2017.
Earlier, Netanyahu applauded Trump's call for nations to do more to fight terrorism during his visit to Saudi Arabia.
While in Saudi Arabia, Trump accused Iran of fuelling "the fires of sectarian conflict and terror" while calling for its worldwide isolation.
Israel and the Palestinians have not held direct talks for more than three years and Trump acknowledged it was "one of the toughest deals of all".