But experts said the United States had little desire to be drawn more deeply into the dangerous proxy war between Iran and the Sunni states playing out in places like Yemen. “The United States is not interested in overindulging in other issues that the gulf states are worried about,” said Marwan Muasher, a Jordanian former foreign minister. “Are the gulf states going to go back from this meeting feeling reassured? I would say the answer is no.”

Presidents have labored to stay close to Saudi Arabia for decades, but have sometimes run into turbulence. Ronald Reagan sold the Saudis sophisticated Awacs airplanes over the objections of Israel. George Bush sent 500,000 troops to defend Saudi Arabia and reverse Iraq’s 1990 invasion of Kuwait. His son George W. Bush shared plans in advance with eager Saudis for his own invasion of Iraq.

But King Abdullah of Saudi Arabia, who died in January, was once so upset with the younger Mr. Bush about his support for Israel that the king threatened to storm out of a visit to the president’s Texas ranch. The Saudis also frustrated Mr. Bush by refusing to work closely with the Shiite-led Iraqi government as it fought Sunni insurgents. Over the years, administrations have worried about Saudi money that has financed extremist groups.

Mr. Obama, who ripped up his schedule to fly to Riyadh in January to pay respects to King Salman when he took power, spoke with the king by telephone on Monday. The White House had announced Friday that King Salman would attend the meeting, but was blindsided over the weekend when the Saudis said they would instead send Crown Prince Mohammed bin Nayef and Prince Mohammed bin Salman.

The Saudis said the king needed to stay in Riyadh because of the kingdom’s air campaign against Houthi rebels in neighboring Yemen. Some regional experts said that at age 79, he has not traveled much out of the country. But some Arab officials said his decision not to attend reflected a broader disappointment that Mr. Obama would not be offering much concrete security assistance at the meeting.

The king was not the only one to turn down Mr. Obama’s invitation. The leaders of Oman, Bahrain and the United Arab Emirates — some of whom are in ill health — will also skip the meeting, sending subordinates instead.

Critics said the list of attendees revealed Mr. Obama’s inability to shape events in the region. “It’s an indicator of the lack of confidence that the Saudis and others have,” Senator John McCain, Republican of Arizona, told MSNBC. He blamed Secretary of State John Kerry for misreading Saudi signals. “He sometimes interprets things as he wants them to be rather than what they really are,” Mr. McCain said.