Trump has described bringing peace between Israelis and Palestinians as "the ultimate deal" and "something that I think is frankly, maybe, not as hard as people have thought over the years".
Trump is on a foreign trip meeting with Muslims, Jews and Christians in an effort to bring peace to the Middle East.
WEST BANK, Palestinian Territories - Israeli forces shot and killed a Palestinian teenager as he allegedly attempted to stab a border police officer at a checkpoint near Bethlehem as US President Donald Trump traveled to West Bank on Tuesday.
"I also look forward to working closely with you to advance peace in our region, because you have noted so succinctly that common dangers are turning former enemies into partners", Netanyahu said.
He stressed that his administration is committed to help both nations to build peace.
The president met earlier Tuesday with Palestinian Authority President Mahmoud Abbas. "But with determination, compromise and the belief that peace is possible, Israelis and Palestinians will reach a deal", he said.
"Iran's leaders routinely call for Israel's destruction", Trump said.
He became the first sitting USA president to visit the site in the Israeli-annexed east of the city.
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"Our real problem is with the occupation and the settlements and Israel's failure to recognize the state of Palestine, as we recognized it, which undermines the achievement of the two-state solution".
Trump was visiting Jerusalem's Old City, just a few miles (kilometres) away, at the time.
Trump had arrived in Bethlehem by motorcade, crossing a checkpoint at Israel's controversial separation wall, and was greeted by Abbas and other dignitaries outside the city's presidential palace.
Israel occupied the West Bank, including east Jerusalem, in the Six-Day War of 1967.
Later in the day, the first lady joined Trump at his meeting with Pope Francis at the Vatican. Trump himself never commented.
During the trip, White House aides downplayed hopes any significant progress on reviving the long-stalled peace negotiations can be made, describing the President's first trip to the region as "symbolic".
While past United States presidents have set out broad principles both sides must meet in order to reach a peace deal, Trump has resisted laying out any clear guidelines, instead promising to act as a mediator and urging both sides to take steps toward peace.
Trump, meanwhile, told Herzog, the Zionist Union leader: "I am serious about a deal and I am determined".
The moment was an abrupt interruption of an otherwise warm and smooth welcome for Trump to the Holy Land.