Trump's trip began in Saudi Arabia and takes him, after Israel, to the Vatican for an audience with Pope Francis, to Brussels for a North Atlantic Treaty Organisation summit and to Sicily for a meeting of leaders of the Group of Seven major industrial nations.
Palestinian president Mahmud Abbas and Israeli Prime Minister Benjamin Netanyahu have not had substantive direct talks since 2010.
A screen on the official White House website previewing upcoming statements by Trump and Netanyahu noted the location as "Jerusalem, Israel". He talked about moving the USA embassy to Jerusalem, and named an outspoken critic of Obama's policies, David Friedman, as US ambassador to Israel.
Trump has backed away from other campaign promises as well.
"Trump has made a crisis between Israeli intelligence and American intelligence", the former official and recruiter tells Newsweek by phone. The caption reads, "A changing of the guard at the Prime Minister Netanyahu's office": Trump is known for his deal-making and his transactional approach to foreign policy.
Former Mossad chief Danny Yatom told CBS News on Wednesday that Israel must "think twice before transferring information to the Americans".
When Netanyahu asked if he could accompany the president, a USA diplomat told the Israelis that the site is in the West Bank and is "not your territory".
Israel reacted with outrage, arguing it could not be the president's position that Netanyahu not visit a site considered one of Judaism's most sacred places.
Eyebrows went up because those views don't reflect the longstanding policy of the USA government.
The Netanyahu government has largely shrugged off the controversies.
"The security relationship between Israel and our great ally the United States is deep, meaningful and unprecedented in its scope and contribution to our strength", Defense Minister Avigdor Lieberman tweeted. "That is how it has been and that is how it will continue to be".
The incident has affected voters' confidence in Trump handling the nation's most sensitive secrets. And at this point, it seems Israelis across the political spectrum have something to worry about.
Despite the Israeli protests, Trump's national security adviser would not back down. Israeli right-wingers rejoiced in Trump's election, believing it would allow them to move ahead with unrestrained settlement building and, for some, to move toward their goal of annexing most of the West Bank.
Trump has been receptive to Israel's position that Palestinian leaders must do more to stop incitement to violence, including by stopping payments to the families of those who have carried out attacks and were killed or are now in jail. Palestinians will use the meeting to bolster a weakened Abbas.
"There is a chance something happens - something good", said Zananiri. "If it doesn't, he'll say 'I tried'".
Israeli Arabs - Christians and Muslims who live in Israel and hold full citizenship - aren't holding their breath either.
Aaron David Miller, a Middle East peace adviser to Democratic and Republican secretaries of state, said that despite Greenblatt's positive reviews in the region, there are limits over how much influence he, or any American officials, can have over the process.
Livni said strong Arab support for a future Israeli-Palestinian deal is a "game changer" that could help sway a skeptical Israeli public.