Mr Trump is visiting Israel and the Palestinian territories, as he continues his Middle East trip.
He flies in from Saudi Arabia, a key US ally, where he gave a speech to Arab and Muslim leaders at a summit.
The US president will hold talks with both Israeli and Palestinian leaders during the course of his two-day stop.
President Trump has called an Israeli-Palestinian peace agreement “the ultimate deal”, but has been vague about what form it should take.
He has said he prefers to leave it to both sides to decide between them in direct talks.
At a summit in Riyadh on Sunday, Mr Trump called on Arab and Muslim leaders to take the lead in combating Islamist militants, urging them to “drive them out of this earth”.
He singled out Iran, saying it had “fuelled the fires of sectarian conflict and terror” in the region for decades.
Donald Trump also stated again that he believed peace between Israelis and Palestinians was possible.
Trump has been widely seen as considerably more supportive of Israel than his predecessor, Barack Obama. He has taken a softer position on the contentious issue of Israeli settlements, suggesting that their expansion rather than their existence might hamper the search for peace.
Over 600,000 Jews live in about 140 settlements built since Israel’s 1967 occupation of the West Bank and East Jerusalem, land Palestinians claim for a future state. The settlements are considered illegal under international law, though Israel disputes this.
Mr Trump has also sent mixed signals on the issue of Jerusalem, pledging to move the US embassy there from Tel Aviv, angering Palestinians and delighting Israelis.
Nevertheless he has since stalled, with Secretary of State Rex Tillerson recently telling NBC News Mr Trump was weighing it up.