In his comments to both Rivlin and Israeli Prime Minister Benjamin Netanyahu, Trump appeared to dwell on forging a regional coalition to counter what he described as Shi'ite Muslim Iran's involvement in conflicts in the region, rather than renewed efforts to revive Israeli-Palestinian peace talks. Trump touched it in prayer and, adhering to tradition, placed a note in a deep crevice.
Mr Trump has already indicated what is on his wish list during his visit to Jerusalem and Bethlehem this week.
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.
Trump will meet Netanyahu at 6:00 pm (1500 GMT).
In the nearby Jewish Quarter, barriers had been erected to make viewing the square impossible from ground level, and some residents said they had been told not to go onto their roofs overlooking the Western Wall.
This is the unexpected cloud that may hang over Trump's visit.
Not as pleasing to Israeli leaders, however, were comments by a junior USA official in the lead-up to the visit, planned for Monday, that the Western Wall is not in Israeli territory but "is part of the West Bank".
The official added, "We are convinced that this view is contrary to the policies of President Trump as can be seen by his strong objection to the last U.N. Security Council resolution", referring to a December resolution that called for an end to Israeli settlements which the Obama administration declined to veto.
Under strict interpretation of Jewish law, men and women must pray separately there. It is considered the holiest site in Judaism.
"The Temple Mount and the Western Wall will always remain under Israel's sovereignty", Netanyahu continued. Sitting at the entrance to his antique silver shop on Sunday, Mohammed Awad complained that the site does not belong to Jews and that the president made a mistake by not visiting the Al Aqsa Mosque.
A screen on the official White House website previewing upcoming statements by Trump and Netanyahu noted the location as "Jerusalem, Israel".
The status of Jerusalem is ultra-sensitive and has been among the most hard issues in Israeli-Palestinian peace talks. Rather, Democratic and Republican administrations have said Jerusalem's status must be solved through US negotiation. The global community says the fate of east Jerusalem, claimed by the Palestinians, must be resolved through negotiations.
For years, the worldwide consensus for a two-state solution has been based on the idea of demilitarised Palestinian state within the 1967 borders, with Jerusalem as its capital.
The traditional American position has been that Jerusalem's status must be negotiated between the two sides.
Trump began his first worldwide trip since taking office in January with a visit to Saudi Arabia on Saturday.
He said the summit in Saudi Arabia "had no political value, and will bear no results". "I'm very happy with the one that both parties like".
"We have travelled here to see the church", he told AFP. An Israeli TV station quoted an American as telling the Israelis that the wall is not in Israeli territory, enraging Trump's Israeli hosts.
"He is our cross (to bear)" he said, holding his arms wide to imitate a crucifixion.
If in the past we believed that peace with the Palestinians would bring about peace with the Arab world, we now hope that the reverse will be true-that peace with Arab states will facilitate peace with the Palestinians.