Japanese Prime Minister Yasuhiro Nakasone, in his first 100 days in office, has suffered a sharp decline in voter popularity as a result of his bid for a stronger Japanese role in its military alliance with the United States.

Many American observers, Nakasone has made impressive strides toward patching up badly tattered relations between the two countries by bluntly and repeatedly stating his determination to have Japan play the part of a more stalwart U.S. ally committed to actively countering the growing Soviet military presence in the Pacific.

At the same time, however, Nakasone's bold pronouncements have sharply diminished his support in Japan, where strong antiwar sentiments are only slowly changing. They have also sowed seeds of conflict within the ruling Liberal Democratic Party.

Any further plunge in Nakasone's popularity, political analysts here say, could seriously threaten his hold on power and his ability to deliver on issues of vital interest to Washington.

The prime minister first sparked a furor here when he declared during an official visit to Washington in January that Japan should become "an unsinkable aircraft carrier" in defense against the Soviet long-range Backfire bomber. In an emergency, he said, Japan should also prevent the passage of Soviet submarines and surface ships into the open waters of the Pacific by bottling up the key straits that go through the Japanese islands.

In February, Nakasone told the Japanese parliament that, in the event of an attack on Japan, Japanese defense forces would take to the high seas to protect U.S. naval vessels coming to the country's aid. Later, he declared that Japan would, if faced with an impending assault, allow U.S. forces to blockade strategic Japanese straits against the Soviet fleet.

Taken together, these statements signaled a rare clear-cut indication of Japan's willingness to expand its definition of military cooperation with the United States in concrete terms under the 31-year-old mutual security treaty between the two countries. Nakasone's predecessors have avoided such commitments, preferring to cloak Japan's obligations under the security pact in hazy words.

Judging by recent public opinion polls here, Nakasone's outspokenness has amplified his long-standing and mostly negative image as a "hawk" on military matters. A survey by the Asahi Shimbun, a major daily newspaper, showed that support for Nakasone has slipped to 29 percent, from 37 percent shortly after he took office on Nov. 26. It registered a similarly sharp drop in his popularity among traditional supporters of his party.

Other samplings showed strong public opposition to Nakasone's endorsement of progressively larger military budgets in coming years and his support of a nationwide review of Japan's American-engineered postwar constitution, which rejects war as an instrument of national policy.

Nakasone's decision in January to permit the export of Japanese military technology to the United States, was supported by only 15 percent of those polled while 69 percent opposed it. The decision was viewed here as the first major shift in Japan's 15-year-old ban on arms exports.

"It is perfectly natural that the public opinion polls show a drop in popularity," said Rei Shiratori, an authority on Japanese politics, "because Nakasone has challenged the . . . basic principles by which the conservative party has run the country since the war."

Inside his party, Nakasone's hard line on defense has ruffled feathers among many politicians who hold to the prevalent attitude here that the country is better served by the postwar division of labor under which, in effect, the United States defends Japan while Japan concentrates on building up its economic strength.

Even influential promilitary elements within the party have expressed growing dissatisfaction with Nakasone for making what they regard as ill-timed statements that have needlessly stirred up adverse public sentiment.

Legislators belonging to the key party faction led by former prime minister Zenko Suzuki, which was instrumental in bringing Nakasone to power, have criticized him openly for roiling the political waters here before important nationwide elections for parliament later this year.

"If I told you we are not concerned," said a source close to the prime minister who did not want to be named, "that would not be true." But had Nakasone failed to move quickly to improve relations with the United States, he asserted, "the mood in the Reagan administration, in Congress, and among the general public regarding Japan would be very bad right now."

Nakasone has attempted, in recent days, to reverse his apparent decline in popularity by shifting from his uncharacteristically high profile on foreign affairs to the bread-and-butter domestic issues that normally command most of Japanese leaders' attention. Stepping back from an earlier government pledge to reject opposition party and labor union calls to cut taxes, Nakasone has promised to enact a major income tax reduction later this year.

He has also stressed the need for a sweeping reform of Japan's antiquated education system after an outbreak of juvenile violence here that has shocked the nation.

While Nakasone has generally created a favorable impression among Japan-watchers in the United States, his support among Japanese has suffered because of his close ties to former prime minister Kakuei Tanaka. Tanaka is awaiting trial this fall on charges of receiving $2.1 million in bribes to influence the sale of Lockheed aircraft in Japan in the early 1970s.