When President Trump shook hands with Syria’s new leader and promised to lift sanctions on his country at the Saudi royal palace this week, it was a vivid demonstration of how the president’s Middle East diplomacy has all but sidelined Israel.

“Tough guy, very strong past,” Mr. Trump said about President Ahmed al-Shara, who once had ties with Al Qaeda. Mr. Trump said he was ending the sanctions, many of which had been imposed on Syria’s previous government, “to give them a chance at greatness.”

In doing so, Mr. Trump was effectively shrugging off the views of Israeli Prime Minister Benjamin Netanyahu, whose government calls Mr. al-Shara a “jihadist.” Israel’s military has bombed Syria hundreds of times since December, when rebels led by Mr. al-Shara ousted President Bashar al-Assad from power.

In recent decades, under U.S. presidents from both parties, Israel has largely enjoyed a special place at the center of American foreign policy in the region. Mr. Netanyahu, who has been in power for much of the past two decades, was always an essential player in the Middle East debate, even as he sometimes infuriated his American counterparts.

There is no indication that the United States is abandoning its historic ties with Israel, or will stop its military and economic support for the country. During his flight on Air Force One from Riyadh to Doha, Mr. Trump dismissed concerns about sidelining Israel.

“No not at all,” he told reporters. “This is good for Israel, having a relationship like I have with these countries, Middle Eastern countries, essentially all of them.”