In this far corner of the world, the Soviet peace and friendship offensive takes form in this message: "Be nice and you can fish in our waters." And increasingly, the Japanese fishermen are starting to agree.

In the fishing cities of Japan's northernmost island, Hokkaido, where the economy rises and falls on the size of catches, the Soviet price varies.

Sometimes it is a cheap bribe exacted from the Japanes fishing boats, such as panty hose or typewriters. Sometimes the Soviets expect information on Japanese defense assigments and operations. Fishermen who give the right kind of information are said to get favorable treatment in lucrative fishing grounds off Soviet-held islands nearby.

Most often, what the Soviets want is an opening on Japanese territory for cultural and trade relations, mixed with a bit of propaganda. Japanese who want trade and fishing rights with the Soviets oblige by building expensive "friendship and culture" halls here and in Wakkanai and Kushiro.

This fish-for-friendship campaign has had a remarkable success in the last three years, since the Soviets imposed a 200-mile fishing zone that barred outsiders from the best fishing grounds. Japan-Soviet friendship groups are sprouting all over Hokkaido, sponsored usually by important businessmen seeking trade and fishing privileges from Moscow. Soviet trade and cultural groups pay regular visits.

The Soviet campaign has alarmed the prefectural government in Hokkaido, where officials acknowledge that fishermen have come to believe that they will get favorable Soviet treatment if they join the Soviet friendship groups.

In an interview, Hokkaido Gov. Naohiro Dogakinai discussed reports from one port, Kushiro, where officials say fishermen who join a pro-Soviet association get a certificate that they think assures them safe passage in Soviet waters.

"The fishermen seem to think that if they are not members of the association, the Soviets will prevent them from taking fish," the governor said. "If that is true, it is a serious problem." Other officials privately said the reports have been verified, although no one wants to discuss the delicate issue on the record.

The Soviet penetration also has alarmed the national government in Tokyo. Soviet economic pressures on Hokkaido, coupled with the growing Soviet military buildup on nearby islands, have fostered fears that a part of Japan could be eventually intimidated and influenced into siding with Moscow on broader issues. The Foreign Ministry is assigning a permanent emissary here to guide the prefectural government on Soviet affairs. Some speak darkly of the potential "Finlandization" of Hokkaido.

(Finland, also a close neighbor of the Soviet Union, is precluded by a treaty concluded under Soviet pressure from adopting an anti-Soviet foreign policy and has followed a course of strict neutrality and absention from military alliances.)

The Kremlin's immediate goal seems to be to deflate the national movement that seeks return of four islands in the Kurile chain to Japanese control. They were seized by Soviet forces at the end of World War II and Japan has been trying to get them back ever since. Soviet officials refuse to negotiate the issue and have fortified one of the islands with approximately 8,000 troops in the last two years.

A citizens' movement seeking return of the islands has been a hotbed of anti-Soviet sympathies for years and Hokkaido is its focal point. To defuse it the Soviets have put out the word that fishermen who support the reversion movement are not welcome in the fishing grounds.

One government official said Soviet representatives have made extensive efforts to gather names of the movement's supporters. The Soviet consul here has requested the Hokkado government to prohibit posting of slogans and signs that support the government.

One of the more vulnerable fishing ports is Wakkanai, on the northern tip of Hokkaido only a few miles from the Soviet island of Sakhalin. Since its fishermen have been barred from the rich catches off Sakhalin, the city has made extensive changes to accommodate Soviet interests in the hope of getting fishing privileges. Virtually the whole city joined in building a Japan-Soviet friendship and culture hall that opened June 21 in a ceremony attended by Soviet ambassador Dmitri Polyansky.

Visitors report that, to keep peace with the Soviet visitors, the city has agreed not to display signs calling for the reversion of the disputed islands. Once a center of anti-Soviet activity, Wakkanai now discourages leaders of the national movement from coming there to stage anti-Moscow rallies. Those who belong to the reversion movement in Wakkanai are branded as hostile by Soviet representatives.

"This is not a happy thing for a fisherman," said a Hokkaido official who has investigated conditions in the town. "What is happening is that fishermen feel that if they take part in the [reversion] movement they will be seen as anti-Soviet and severely treated if they are caught" fishing illegally, he said. "The trend is to be careful. If the movement wants to hold a meeting in Wakkanai, the people there are very negative."

The man spearheading the pro-Soviet movement in Wakkanai is Tsunezo Seto, head of the main fishing organization and chairman of the chamber of commerce. He is not eager to discuss his town's transformation and he answered questions in a gruff voice recently when pursued along the streets of Sapporo.

He was asked if fishermen who join his Soviet friendship association and new culture hall are given favorable treatment by Soviet patrol boats when they head toward forbidden waters off Sakhalin.

"That is not the condition," he replied. But if the Soviets "out of good will" treat members favorably, "then it is all right with us," he added. Seto irritably denied that his group tries to discourage the reversion movement. "Who told you that?" he asked.

The Soviets' leverage over Japanese fishermen stems from their practice of inflicting stiff penalties on those caught fishing near Soviet-held islands. Punishment ranges from two or three days in a detention center on Shikotan Island to long prison terms in Sakhalin or Siberia. Some have been sentenced to five-year terms. Large fines are exacted from those caught. More than 1,600 Japanese fishing boats have been seized since 1946.

In the past few yers, authorities here say, the Soviet patrols have offered the fishermen several knds of bargains. They offer lenient treatment in exchange for petty bribes of commodies hard to get in the Soviet Union.

But some Japanese have provided a quasi-espionage role in exchange for fishing rights. So-called "reporter boats" have been known to provide information on the size, movement, equipment, and operations of Japan's defense forces in Hokkaido.

The Soviet techniques have caused public division in some fishing ports. For years, they were centers of anti-Soviet hostility because many people had settled in them as emigres from the Soviet-held Kurile Islands. Now they are being forced to deal with the Soviets in order to get back to their old grounds.

One city of divided feelings is Nemuro on the eastern coast a few miles from the Kurile chain. Passions run high for getting the islands back, said Minoru Shinde, until recently a Hokkaido provincial fisheries official there.

"But the people are very sesitive to the fact that their boats can be caught and checked and forced to pay fines," he said. "So they do not want to excite the Soviets."

The Soviet penetration has formally reached a peak in Kushiro. A large number of fishermen have joined the Soviet friendship association and for about $50 they get a certificate of membership. Reliable sources say that if the fisherman shows the certificate to Soviet patrols when he is stopped at sea, he is guaranteed lenient treatment. If arrested, he is released with a light fine.

The founder of that association is Masaharar Muto, who has prospered from a rich timber trade with the Soviets and is the chief welcomer for many Soviet delegations. He denied in an interview that his association certificate guarantees easy treatment from the Soviets. It only helps overcome language problems with Soviet patrols, he said, and shows the Soviets that the certificate's owner is "friendly." It does not, however, guarantee freedom from Soviet prosecution, he said..