What seems clear, analysts said, is that while Japanese were sympathetic to putting the relationship on a more equal footing, they shied away from more fundamental changes, in a country that still views Washington as a largely benign protector.

“The Japanese public was not willing to follow Hatoyama down this path of Futenma and changing the alliance,” said Izuru Makihara, a professor of politics at Tohoku University in Sendai, Japan, referring to the American base, United States Marine Air Station Futenma. “The consensus is that Japan needs the United States, with China and North Korea nearby.”

Mr. Hatoyama’s sudden departure left his Democratic Party scrambling to find a new leader to restore a sense of direction for a party that had swept into power with high hopes last summer in a landslide. The party’s control of Parliament’s Lower House ensures it will hold on to power despite the resignation.

Party members gathered behind closed doors to select candidates for an internal party vote on Friday that will elect Mr. Hatoyama’s successor. The finance minister, Naoto Kan, 63, a former leader of the Democratic Party, emerged as an early frontrunner.

As the party moves to choose Japan’s sixth prime minister in four years, many in Japan see Mr. Hatoyama as having frittered away his party’s historic electoral mandate on the seemingly minor issue of relocating a single American military installation.

In truth, his government faltered on a host of issues, including scandals over political financing; an inability to deliver on other campaign promises like eliminating highway tolls; and the party’s failure to focus on pocketbook issues affecting voters, like unemployment or Japan’s anemic growth rates.

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Still, Mr. Hatoyama’s handling of the base issue seemed to crystallize all that went wrong with his short-lived government, including what many Japanese saw as its fatal flaw: his own indecisiveness. The prime minister seemed to waffle between appeasing Washington and assuring Okinawans that he would honor his campaign vows.

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During last summer’s election campaign, Mr. Hatoyama pledged to end Japan’s dependence on the United States, and improve ties with China and the rest of Asia. His fall is a blow to China, which had hoped to expand its influence in Japan.

The centerpiece of Mr. Hatoyama’s push was a pledge to move the Futenma base and its noisy helicopters off Okinawa. But Mr. Hatoyama ran into fierce resistance from the Obama administration. Eager to establish that the United States was not retreating from Asia, it refused to back down from a 2006 agreement to relocate the base to a less populated part of the island.

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During a visit to Japan last October, Defense Secretary Robert M. Gates made it clear he had no intention of reopening negotiations.

Public opinion turned against Mr. Hatoyama’s handling of Japan’s crucial relationship with Washington. His government’s approval ratings plummeted from more than 70 percent in September to the high teens in recent weeks.

In the end, the lack of support, and what Mr. Hatoyama called his belated recognition of the importance of the Marines as a deterrent, forced him to accept most of the 2006 agreement. He resigned a week later, as he appeared to be a heavy liability for the Democrats facing parliamentary elections on July 11.

Analysts say that the public did not reject all aspects of Mr. Hatoyama’s agenda. His calls for building a more equal relationship with the United States resonated in Japan, which has grown weary of its junior status in the alliance.

“Hatoyama tapped into the feeling of many Japanese that it is time to rethink their nation’s place in a changing world,” said Takashi Kawakami, a professor who specializes in security issues at Takushoku University in Tokyo. “But wanting to be treated as an equal by Washington is not the same as wanting to be independent of Washington.”

A curious aspect to Mr. Hatoyama’s fall is that for decades the United States has sought to loosen the Liberal Democratic Party’s hold on the country. But the two governments that succeeded in doing so — one in 1993-94, and the current one — simply could not pull the levers of power, leaving American officials deeply frustrated.

Once a new leader is in place, “I do think there will be a desire to exhibit a different kind of management from the outset,” said a senior administration official, who spoke on condition on anonymity because he was not authorized to speak publicly.

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Analysts said there were lessons in Mr. Hatoyama’s fall for the Obama administration. Sheila A. Smith, a senior fellow for Japan studies at the Council on Foreign Relations, said American officials did not initially show enough patience with the new government. “There was responsibility on both sides,” she said.

One immediate upshot of Mr. Hatoyama’s failure will most likely be that his successor will avoid making big changes in foreign policy, in favor of focusing on domestic issues.

“Hatoyama self-destructed on Futenma,” said Mr. Kawakami of Takushoku University. “His successor is not going to want to touch that issue.”