Since taking office, Trump has edged away from unqualified backing for Netanyahu's drive for more Jewish settlement in territory the Palestinians claim for a state, and also from a pledge to move the American embassy from Tel Aviv to Jerusalem.
But Netanyahu remained upbeat as he prepared to fly out from Tel Aviv airport today.
"The alliance between Israel and America has always been extremely strong. It's about to get even stronger," the prime minister said.
Mark Heller, a political scientist at the Institute for National Security Studies (INSS) in Tel Aviv, said the embassy issue was "marginal, to the extent that such a promise is unlikely to be kept".
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The prospect of a Trump rethink challenges the hopes of the settler lobby, a driving force in Netanyahu's right-wing coalition government, and others on the Israeli right who want to see at least partial annexation of the West Bank.
In an interview published on Friday in the pro-Netanyahu daily Israel Hayom, Trump said settlement growth was not "good for peace".
Around 600,000 Israelis currently live in settlements in the occupied West Bank and east Jerusalem, communities considered illegal by the United Nations and most world powers.
"In Washington, Benjamin Netanyahu will test his room to manoeuvre (with Trump) on settlements," Heller told AFP.
"For (the past) three weeks Donald Trump has been speaking differently," said Michael Oren, deputy minister in charge of diplomacy in Netanyahu's office. "We must act cautiously."
Netanyahu himself said at Sunday's weekly cabinet meeting that strengthening Israel's ties with its historic ally "requires a responsible and considered policy, and that is how I intend to act".