In a stopover lasting 28 hours, Trump is to meet separately with Israeli Prime Minister Benjamin Netanyahu and Palestinian President Mahmoud Abbas. Later on Monday, he will pray at Judaism's Western Wall and visit the Church of the Holy Sepulchre in Jerusalem, and on Tuesday he will travel to Bethlehem.
Netanyahu and his wife Sara, as well as President Reuven Rivlin and members of the Israeli cabinet, were at Tel Aviv's Ben-Gurion airport to greet Trump and first lady Melania in a red carpet ceremony after what is believed to have been the first direct flight from Riyadh to Israel.
"During my travels in recent days, I have found new reasons for hope," Trump said in a brief speech on arrival.
"We have before us a rare opportunity to bring security and stability and peace to this region and its people, defeating terrorism and creating a future of harmony, prosperity and peace, but we can only get there working together. There is no other way," he said.
Trump's tour comes in the shadow of difficulties at home, where he is struggling to contain a scandal after firing James Comey as FBI director nearly two weeks ago. The trip ends on Saturday after visits to the Vatican, Brussels and Sicily.
Netanyahu said Israel shared Trump's commitment to peace - but he also repeated his right-wing government's political and security demands of the Palestinians, including recognition of Israel as a Jewish state.
"May your first trip to our region prove to be a historic milestone on the path towards reconciliation and peace," Netanyahu said.
US Secretary of State Rex Tillerson told reporters en route to Tel Aviv that any three-way meeting between Trump, Netanyahu and Abbas was for "a later date".
Trump has vowed to do whatever is necessary to broker peace between Israel and the Palestinians -- something he has called "the ultimate deal" -- but has given little indication of how he could revive negotiations that collapsed in 2014.
When he met Abbas this month in Washington, he stopped shortly of explicitly recommitting his administration to a two-state solution to the decades-old conflict, a long-standing foundation of US policy. He has since spoken in support of Palestinian "self-determination".
Trump has also opted against an immediate move of the US Embassy in Tel Aviv to Jerusalem, a longtime demand of Israel.
"We're having very good discussions with all parties and, as long as we see that happening, then we don't intend to do anything that we think could upset those discussions."
Netanyahu has come under pressure from right-wing members of his own coalition who say he is not pushing hard enough to get Trump to carry out his promise.
Over the weekend, Trump received a warm welcome from Arab leaders, who focused on his desire to restrain Iran's influence in the region, a commitment they found wanting in the Republican president's Democratic predecessor, Barack Obama.
On Sunday, Israel authorised some economic concessions to the Palestinians that it said would improve civilian life in areas controlled by the Palestinian Authority and were intended to respond to Trump's request for "confidence-building steps".
The United States welcomed the move but the Palestinians said they had heard such promises before.
Trump used his visit to Riyadh to bolster US ties with Arab and Islamic nations, announce $110 billion in US arms sales to Saudi Arabia, and send Iran a tough message.
In a speech on Sunday to dozens of Arab and Islamic leaders, he toned down the harsh anti-Muslim rhetoric he had employed during his presidential campaign in favour of trying to build cooperation against Islamist terrorists.
"A better future is only possible if your nations drive out the terrorists and drive out the extremists. Drive them out," Trump said.
Trump will have visited significant centres of Islam, Judaism and Christianity by the end of his trip, a point that his aides say bolsters his argument that the fight against Islamist terrorism is a battle between "good and evil".
(Reporting by Steve Holland and Jeff Mason; Additional reporting by Ori Lewis in Jerusalem; Editing by Kevin Liffey)
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