"I wanted you to know how much we appreciate the American change in policy on Iran," Netanyahu said as the two leaders delivered joint statements at the prime minister's residence here, but took no questions from reporters.
"We can hold back Iran's march in this region and thwart Iran's unbridled ambition," Netanyahu added.
Trump said he wanted to work with Netanyahu to take on the "threat of (the) Iranian regime...causing so much violence and suffering."
With Trump standing beside him, Netanyahu also called Jerusalem the united and eternal capital of Israel and said Israel protects the holy sites of Judaism, Christianity and Islam.
He thanked Trump for becoming first sitting U.S. president to visit the Western Wall.
"You noted so succinctly that common dangers are turning former enemies into partners, and that is where we see something new and potentially very promising," Netanyahu said of possible peace with the Palestinians, nothing the "reassertion of American leadership in the Middle East."
"It will not be simple, but for the first time in many years, and the first time in my lifetime, I see a real hope for change," the prime minister added.
For his part, Trump said he wanted to reaffirm the "unbreakable bond of friendship" between the two nations and told Netanyahu that he was "deeply moved" by his visit to the Western Wall earlier Monday.
"It will leave an impression on me forever," Trump said.
"We want Israel to have peace," the president added, saying of the Israeli prime minister, "He's working very hard at it. It's not easy ... America stands ready to assist in every way we can."
Trump continued, "We can truly achieve a more peaceful future for this region and for people of all faiths and all beliefs and frankly all over the world...There's a lot of love out there."
Before the statements, Trump signed the guest book at the prime minister's residence and wrote a message. Both leaders were joined by their wives.
"Welcome to our palace," said Netanyahu, who showed the Trumps a 150-year-old Bible displayed at the residence.
Earlier Monday, after arriving in Israel, Trump said he was "very, very honored" to be visiting the country.
"We have before us a rare opportunity to bring stability, security and peace to this region and its people — defeating terrorism," he said.
Trump's two-day visit will also include a meeting with Palestinian Authority President Mahmoud Abbas in Bethlehem and a visit to the Holocaust memorial Yad Vashem on Tuesday.
"I want to see peace with Israel and the Palestinians," the president told Reuters before meeting with Abbas earlier this month at the White House. "There is no reason there's not peace between Israel and the Palestinians — none whatsoever."
White House aides have played down expectations for significant progress on the peace process during Trump's stop, casting it as more symbolic than substantive.
The last round of peace talks, led by then-President Barack Obama and his secretary of state, John Kerry, fell apart in 2014.
While en route to Tel Aviv from Riyadh, Saudi Arabia, Secretary of State Rex Tillerson said president was seeking unity in the fight against terrorism, as well as an opening step in the quest for peace.
"I think he feels like there's a moment in time here," Tillerson said, referring to Trump. "We have the opportunity to advance the peace discussions between the Israelis and the Palestinians…I think the president has indicated he's willing to put his own personal efforts into this if the Israelis and the Palestinians are ready to be serious about engaging as well."
In his welcoming remarks to Trump after Air Force One landed, Netanyahu said, "Israel's hand is extended in peace to all of our neighbors, including the Palestinians."
Palestinian activists, however, are calling for a "Day of Rage" when Trump visits the West Bank on Tuesday. The demonstrations are meant to draw attention to a month-long hunger strike by hundreds of prisoners being held by Israel, and to protest what many Palestinians say is unfair U.S. support for Israel.
Trump's first foreign trip began in Saudi Arabia and takes him, after Israel, to the Vatican for an audience with Pope Francis, then on to Brussels for a NATO summit and finally to Sicily for a meeting of leaders of the Group of Seven major industrial nations.
Monday's flight — direct from Riyadh to Tel Aviv — was in itself historic. It marks the first time Air Force One was able to fly directly between the two nations, which do not have diplomatic relations.
Netanyahu said he hoped "that one day an Israeli prime minister will be able to fly from Tel Aviv to Riyadh."