When Prime Minister Benjamin Netanyahu met President Trump at the White House in February, the two men could not have been more in sync. The president had designated Houthi militants in Yemen as a terrorist organization. They both spoke of stopping Iran from acquiring a nuclear bomb. Mr. Trump even mused about expelling Palestinians from Gaza.

“You say things others refuse to say,” Mr. Netanyahu gushed in the Oval Office, with cameras running. “And then, after the jaws drop, people scratch their heads. And they say, ‘You know, he’s right.’”

Two months later, in another White House visit, Mr. Netanyahu sat almost silently next to the president for more than a half-hour as Mr. Trump expounded on topics having nothing to do with Israel.

That meeting, in April, underscored a growing divide between the two men, who are increasingly in disagreement on some of the most critical security issues facing Israel.

In an April meeting at the White House, Mr. Netanyahu sat silently for more than a half-hour as Mr. Trump talked about issues unrelated to Israel.Credit…Eric Lee/The New York Times

As Mr. Trump heads this week to the Middle East for his first major foreign trip, the president has, for now, rejected Mr. Netanyahu’s desire for joint military action to take out Tehran’s nuclear abilities. Instead, Mr. Trump has begun talks with Iran, leaving Mr. Netanyahu to warn that “a bad deal is worse than no deal.”