This time, the encounter was more serious, particularly given that a Chinese fighter jet collided with a United States Navy spy plane in April 2001 in the skies above Hainan Island. The Chinese pilot was killed, and the American plane was forced to make an emergency landing on Hainan.

After the collision, the Chinese authorities detained the American crew for over a week and initially issued an angry statement saying that “the U.S. side has total responsibility for this event.”

Adm. Dennis C. Blair, then commander in chief of the United States Pacific Command, issued his own angry statement, charging that the Chinese plane had been tailing the American jet, a practice Beijing’s military had increasingly adopted. “It’s not a normal practice to play bumper cars in the air,” Admiral Blair said at the time.

China has continued to show off its military prowess to the United States in the 13 years since the Hainan collision. In 2011, when Defense Secretary Robert M. Gates visited China, the military there greeted him with an unexpected and, in the view of American military officials, provocative test of a stealth fighter jet. The bold show of force surprised the Americans and also, it appeared, the Chinese president, Hu Jintao.

This year, when Defense Secretary Chuck Hagel visited China, the military greeted him with a tour of the country’s lone aircraft carrier, the Liaoning, that the United States government had long sought. American officials interpreted that visit as another indication of China’s resolve to project its naval power.

In part, military analysts say, China wants to assert power over nearby seas and its airspace because of tensions with its neighbors over disputed islands in the East and South China Seas.

Admiral Kirby said there was no “Machiavellian intent” in the three-day delay in reporting the confrontation this week. “I think we needed to process the information and kind of figure out what really happened,” he said. “And I also believe — and I think this was the right course, too — we wanted to make sure that we had taken the opportunity to register our deep concern.”

“It made no sense to go public with that until we had a chance to deliver that démarche, which we did,” he added.