And the interests of the two countries tend to diverge on other issues, especially combating Al Qaeda and other extremist organizations, which receive some of their funding from Saudi sources. “I think the Saudis and the Americans have developed the habit of coexisting with their disagreements,” said Khalid al-Dakhil, a political-science professor in Riyadh, the Saudi capital.

White House officials said they were confident that the United States and Saudi Arabia would continue to work together on a range of issues, including the fight against the Islamic State and the response to the recent instability in Yemen. And they said the relationship had improved in recent months, in part because of Mr. Obama’s decision to launch airstrikes against the Islamic State, a campaign that Saudi Arabia has joined and that King Salman’s ascension to the throne was not expected to derail.

Image Rey Salman de Arabia Saudita en el funeral de su predecesor y medio hermano. Credit... Saudi Press Agency

“We are much closer now,” a senior administration official said, speaking on the condition of anonymity. “I wouldn’t say we are completely aligned, but it’s far less than it was at times.”

Others are not so sure.

“The recent shift in Saudi regional and foreign relations is not how outspoken it has become, but how muscular it has become,” said Fawaz A. Gerges, a professor of international relations at the London School of Economics and Political Science. “It has long prided itself on acting behind the scenes.”

An annual “intelligence” dinner at a hotel in Washington every year illustrates that point. The host is the Saudi ambassador to the United States, Adel al-Jubeir, the guests a group of American and Arab spies and intelligence officials, Middle East policy experts and top national security officials in the American government like John O. Brennan, the C.I.A. director who served as the agency’s Saudi Arabia station chief in the late 1990s. Save welcoming remarks by Mr. al-Jubeir, there is no set program, no keynote speech, just high-level national security officials and foreign policy experts networking. Attendees describe the affairs as a Saudi show of force.

“There’s no desire even to talk to the gathered public,” said one foreign policy expert who attended last year’s dinner, speaking on the condition of anonymity because he didn’t want to lose his invitation to this year’s dinner. “The point seems to be to say, ‘Hey, we can get 300 important people in a room. Now let’s move on.' ”