Yad Vashem and Masada are both highly popular tourist destinations, but they will be placed under lockdown for the president's visit.
It is highly unusual for a new envoy to visit the holy site just hours after arriving in Israel.
The now-confirmed new ambassador to Israel, David Friedman, is due to take up his duties from Monday.
Trump, who will meet with Israeli Prime Minister Benjamin Netanyahu in Jerusalem on May 22 and Palestinian President Mahmoud Abbas in Bethlehem on May 23, has stopped short of recommitting to the goal of Palestinian independence, a longtime bedrock of USA policy.
"I can live with either one", Trump said then at a joint press conference with visiting Israeli Prime Minister Benjamin Netanyahu.
Jerusalem Online reported that the operation to secure Trump is codenamed "Blue Shield". It said the comment prompted shouting from the Israeli preparatory team.
Israel occupied the West Bank, Gaza Strip and East Jerusalem in 1967.
Brigitte Macron. Silvio Berlusconi la qualifie de "jolie maman" d'Emmanuel Macron
Brigitte Macron est régulièrement la cible d'attaques sexistes, en raison de la différence d'âge qui la sépare d'Emmanuel Macron. Dans un premier temps, Silvio Berlusconi s'est montré plutôt élogieux à l'égard du nouveau président français.
Rivlin called on the "whole world to recognise Jerusalem as the official capital of the state of Israel". Palestinians also claim Jerusalem as the capital of a future Palestinian state and past peace proposals have proposed splitting the city between East and West Jerusalem, or creating an internationally governed city. The Old City is also home to the Al Aqsa Mosque, the third-holiest site in Islam. Current US policy is that East Jerusalem's status should be determined by Israeli-Palestinian negotiations.
In January, Palestinian Authority President Mahmoud Abbas warned Trump that moving the embassy would have a "disastrous impact on the peace process, on the two-state solution and on the stability and security of the entire region". After stopping in Saudi Arabia, Trump will visit both Israel and the Palestinian territories, in a nod to his nascent bid to strike the Israeli-Palestinian deal that has eluded his predecessors. "Israel has made contact with the United States on this matter", the official said.
Israel's Channel 2 reported Monday that the US delegation rejected Israeli requests that Prime Minister Benjamin Netanyahu and an Israeli TV crew accompany President Donald Trump on his visit to the Western Wall.
Friedman, a fundraiser for settlement causes and vocal critic of liberal Jewish groups, has backtracked from some of his controversial positions.
Spokesman Micky Rosenfeld told the Post: "The second option means hundreds of officers along Route 1 [a highway connecting Tel Aviv to Jerusalem]".
"Everyone I've spoken to in DC that has been briefed on #Jerusalem embassy move says #Netanyahu told #Trump not to move embassy at this time", Powell tweeted. The notes were released on Monday by Mr Netanyahu's office.
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