For China, it appears to be an effort by President Xi Jinping to exercise a degree of control over all sources of national power that his immediate predecessor, Hu Jintao, never fully mastered. Interestingly, as China sent its aircraft carrier to another potential trouble spot, the South China Sea, its path avoided the disputed islands, perhaps a sign that the Chinese realize they may have overplayed their hand.

Still, in private, American officials say they are worried that a small incident — a collision like the one between an American intelligence plane and the Chinese air force a dozen years ago off Hainan Island — could rapidly worsen the situation.

On ABC’s “This Week” on Sunday, Tom Donilon, who was Mr. Obama’s national security adviser until earlier this year and a principal architect of the administration’s approach to China, said a similar “risk of miscalculation” is what “we need to be very concerned about going forward here.” A senior administration official said Mr. Biden’s message would be that the United States will “seek crisis management mechanisms and confidence-building measures to lower tensions and reduce risk of escalation or miscalculation.”

But one of Mr. Obama’s current advisers said, “It’s pretty clear this isn’t really about the islands.” Declining to speak on the record about a sensitive strategic issue, the official added that it was about a desire by some in China, including the People’s Liberation Army and perhaps the new political leadership, “to assert themselves in ways that until recently they didn’t have the military capability to make real.”

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The adviser added: “They say it’s in response to our efforts to contain them, but our analysis is that it’s really their effort to push our presence further out into the Pacific.”

In fact, on his last trip to Asia as secretary of defense, Robert M. Gates said in January 2011 that he believed the long-term goal of the Chinese was to push the United States to “the second island chain,” farther out in the Pacific, keeping American air and naval assets ever farther from the region around China’s coast. Two years later, Obama officials will not utter that view in public, but it is a running theme in American intelligence assessments about the Chinese military, tempered by evidence that some Chinese officials worry about blowback if they overreach.