To cries of "banzai" from a cheering crowd of several hundred, Prime Minister Zenko Suzuki carried Tokyo's campaign for four Soviet-held islands to a rocky bluff within sight of them today amid a growing public outcry for their return to Japan.

Suzuki, goaded by rightists within his party, is the first Japanese leader to make such a trip while in office, underscoring the strength of popular sentiment on the issue, which has strained relations between Tokyo and Moscow for 35 years, and the political pressures on himself.

His trip was a symbolic gesture meant to point up Tokyo's mounting dissatisfaction with the Soviet military buildup on the islands, seized after World War II, and its moves to strike a tougher public posture on the issue. It also reflects a bid by Suzuki to appease a group of powerful politicians on his party's right wing to shore up his shrinking political support.

Echoing local sentiment here, Suzuki called the early return of the islands "Japan's most fervent desire." Moscow now claims that the territorial issue between the two countries does not exist and refuses to talk about it. Suzuki said this was "deeply regrettable" but pledged continuing efforts "to seek a dialogue" on the issue.

The prime minister's visit is the most recent and highly publicized event in a government-sponsored, nationwide campaign for reversion. It started when the Suzuki Cabinet proclaimed a "Northern Territories Day" last February and has been highlighted by rallies, parades and TV commercials demanding the return of the islands.

The Soviet Union has charged that such efforts are aimed at whipping up anti-Soviet hostility in Japan. Suzuki's trip touched off a fusillade of Soviet propaganda and last week Pravda, the official Communist Party newspaper, warned those in Japan "who are seeking to push Japan back onto a dangerous course" toward militarism. A Soviet patrol boat appeared off the coast here today, apparently to register disapproval of the prime minister's presence.

Suzuki's Liberal Democrats, among whom his support is ebbing, have taken up the reversion drive with gusto and organized a series of party-sponsored rallies throughout the country this summer. Last week, 2,700 party members, including six Cabinet ministers and leading party officers attended a gathering in Tokyo calling for the withdrawal of Soviet troops and return of the islands to Japan. In a strongly worded address, party Secretary General Yoshio Sakarauchi charged that the Soviet Union was "holding the knife at Japan's throat."

The dispute over the four islands, off the northeastern tip of Hokkaido, has been a major obstacle in Japan-Soviet relations since the end of World War II and a rallying point for Japanese public opinion.

For a while, Tokyo appeared to be avoiding a showdown that might upset relations with Moscow and a burgeoning trade between the two countries from which many Japanese businesses profit. But relations took on a deep chill after the Soviet invasion of Afghanistan and Japanese economic sanctions against Moscow.

The Soviets now have a division of troops stationed on one of the northern islands and the expanded military presence has set tempers flaring in government and political circles here and touched off moves by private groups seeking reversion. A nationwide petition drive has collected more than 20 million signatures.

Against that background, the Liberal Democrats have, according to one political analyst in Tokyo, struck on reversion as the "ideal issue." Strengthened by the party's landslide victory in general elections last year, its leaders now feel more confident in promoting their conservative policies. A harder line on the Soviet occupation of the islands is the one issue on which the nation's opposition parties dare not disagree because of its widespread appeal to Japanese voters, he said.

Internationally, he said, "it's wise for Japan to show that we are doing a lot in opposing the Soviet Union," particularly because of the Reagan administration's tougher posture.

Among the leading promoters of the reversion drive are members of the conservative party's right wing, who view the movement as a vehicle to promote hawkish views endorsing a stronger military posture for Japan in contrast to Tokyo's official line favoring only modest increases in defense spending.

At the official level, meanwhile, Tokyo has been forced to tread a fine line between its claims to the islands and the need to keep the reversion movement within bounds of its foreign policy considerations.

So far, there appears little danger that the current groundswell of public sentiment here will spill over into a serious political confrontation with the Soviet Union.

What is important, he said, is getting the Soviets to take Japan seriously because "the history of Japan-Soviet relations . . . is the constant Soviet underestimation of Japanese power."