Trump has also retreated from a campaign pledge to move the U.S. Embassy in Israel from Tel Aviv to Jerusalem, bending to the same diplomatic and security concerns as other presidents who have made similar promises.
"Just so you understand, I never mentioned the word or the name Israel", Trump said Monday at a photo op with Netanyahu at Jerusalem's King David Hotel on the second leg of his first overseas trip as president.
"Young Israeli and Palestinian children deserve to grow up in safety, and to follow their dreams free from the violence that has destroyed so many lives", said Trump, in remarks alongside Israeli President Reuven Rivlin in Jerusalem on Monday. In the afternoon, at about 6 pm, he is scheduled to meet with Netanyahu and then dine at the prime minister's residence at a gala night.
Israel occupied east Jerusalem, where the Western Wall is located, and the West Bank in 1967 in moves never recognised by the worldwide community.
Saudi Arabia and other Sunni-majority countries in the Middle East have grown closer to Israel behind the scenes in recent years, united by an equally wary perception of Iran due to its nuclear ambitions and destabilizing actions in the region.
Meeting Netanyahu in Jerusalem, Trump said Iran felt "emboldened" by the worldwide nuclear deal, promoted by Obama, that it signed in 2015 under which it agreed to limit its atomic programme in return for sanctions relief.
President Donald Trump arrived in Israel for a whirlwind 28-hour visit, saying his trip to the region has given him "new reasons for hope".
Trump's foreign tour comes in the shadow of difficulties at home, where he is struggling to contain a scandal after firing James Comey as Federal Bureau of Investigation director almost two weeks ago. He also toured the Church of the Holy Sepulchre, which is believed to be where Jesus was crucified and the location of his tomb.
The president was received warmly in Riyadh and Tel Aviv, and was scheduled to visit Bethlehem in the West Bank for a meeting with Palestinian Authority President Mahmoud Abbas.
Trump was joined by first lady Melania Trump, his son-in-law Jared Kushner and daughter Ivanka Trump. But for all of Trump's confidence, he's dropped very few hints regarding his approach or his administration's policy.
The visit raised questions about whether the US would indicate the site is Israeli territory.
Trump also reportedly told Netanyahu that intelligence cooperation between the two allies is "terrific". After hosting Abbas at the White House in March, Trump boldly stated that achieving peace is "something that I think is, frankly, maybe not as hard as people have thought over the years". "And if you both are willing, we're going to make a deal".
One point of contention in the talks: the fate of east Jerusalem, which Israel captured in the 1967 Mideast war.
Past US presidents have visited the wall, but either before or after their tenure as president. He has taken a tougher line on settlements than Israeli officials had expected, urging restraint though not calling for a full halt to construction.
"The wall is part of Jerusalem", he said, declaring an undeniable fact accepted by all sides.