Saudi Arabia doesn't recognize Israel and the two states don't have diplomatic relations.
After Trump landed in Tel Aviv, Israeli Prime Minister Benjamin Netanyahu expressed "hope that one day an Israeli prime minister will be able to fly from Tel Aviv to Riyadh".
But earlier in the day on Sunday, Netanyahu told a large crowd that Jerusalem will always be the capital of Israel.
Donald Trump has arrived in Israel, the second destination on his five-stop Middle East trip.
U.S. President Donald Trump, right, and first lady Melania Trump board Air Force One for Israel, the next stop in Trump's global tour, at King Khalid worldwide Airport, Monday, May 22, 2017, in Riyadh.
The only direct flights from Israel to Arab states are to Egypt and Jordan, both of which signed peace treaties with Israel.
During Mr Abbas' visit to the White House earlier this month Mr Trump said that a lasting peace agreement is "maybe not as hard as people have thought over the years", although his comments were met with skepticism by many observers.
Trump on Tuesday will head to Bethlehem, a Palestinian territory, where he will visit the Church of Nativity and hold a meeting with Palestinian President Mahmoud Abbas. U.S. Secretary of State Rex Tillerson, speaking to reporters on Air Force One, said the U.S. could provide clarifications to Israel about what happened but said, "I don't know that there's anything to apologize for".
"The Temple Mount and the Western Wall will always remain under Israeli sovereignty", Netanyahu said.
But Trump may face concerns from Israelis over the new $110 billion arms deal he announced during his previous stop in Saudi Arabia as well as questions from Israeli officials about revelations that he disclosed sensitive Israeli intelligence to Russian officials.
Most countries consider all Israeli settlements, including those built with official sanction, to be illegal.
Despite his pro-Israeli campaign trail rhetoric, since entering the White House Mr Trump has caught some Israeli hard-liners off guard with the suggestion the government should "hold back" on settlement building, and his administration has equivocated over whether the USA embassy will move from Tel Aviv to Jerusalem as promised.
Israel considers the entire city to be its capital while the global community says the future of east Jerusalem, claimed by the Palestinians, must be resolved through negotiations.
And on the eve of Trump's visit, an Israeli official said Netanyahu's cabinet has approved confidence building measures with the Palestinians, including allowing building in a West Bank area.
In Saudi Arabia, the president called on the Muslim world to combat radicalization.