He flew in from Saudi Arabia, a key US ally, where he gave a speech to Arab and Muslim leaders at a summit.
Mr Trump will hold talks with both Israeli and Palestinian leaders.
He has called an Israeli-Palestinian peace agreement "the ultimate deal" but has been vague about what form it should take, saying he prefers to leave it to both sides to decide between them in direct talks.
The two-day visit to Israel forms part of Mr Trump's first foreign trip as US president.
Iran must also "cease its deadly funding, training and equipping of terrorists and militias", he said at President Rivlin's residence.
Tehran insists it does not want nuclear weapons but Israel and the US refuse to believe its denials, with fear and distrust of Iran widespread in Israel.
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