But now, as American officials have distanced themselves from the Budapest Memorandum in light of Russia’s takeover of Crimea, calling promises made in Budapest “nonbinding,” the United States is being forced at the same time to make reassurances in Asia. Japanese officials, a senior American military official said, “keep asking, ‘Are you going to do the same thing to us when something happens?’ ”

For Defense Secretary Chuck Hagel, who arrived in Tokyo on Saturday for two days of talks with Japan’s leaders, including Prime Minister Shinzo Abe, America’s longstanding promise to protect Japan against hostile nations — read China and North Korea — has suddenly come under the microscope. The American response to the Russian takeover of Crimea, which President Obama has condemned while at the same time ruling out American military action, has caused deep concern among already skittish Japanese officials.

“The Crimea is a game-changer,” said Kunihiko Miyake, a former adviser to Mr. Abe who is now research director at the Canon Institute for Global Studies in Tokyo. “This is not fire on a distant shore for us. What is happening is another attempt by a rising power to change the status quo.” He pointed as an example to China’s challenge to Japanese control of the Senkaku Islands, the uninhabited rocks in the East China Sea that Beijing claims under the name Diaoyu Islands.