TOKYO (AP) _ Chinese students abroad are trying to extend their stays in their host countries because of the crisis in their homeland, which has turned thousands of exchange students into potential exiles.

The Chinese government's violent suppression of a student-led reform movement has sent a shiver around the world, instilling fear in some students who had hoped to return home and hope in others who want to stay abroad.

Since the June 3-4 military attack on unarmed students in Beijing, governments have said they would extend the visas of Chinese students. Among those are the United States, Japan, Canada and the 12-nation European Economic Community.

In Australia, the Immigration Department said it had received 10,000 inquiries from Chinese students - virtually all of the 10,600 registered in the country - about extending their visas.

Only a few have actually applied, said immigration spokeswoman Jenny Hoskin. ''But we expect a great deal more in coming weeks.''

''We would consider sympathetically the case of any student who could be considered in any sense in danger by returning to China,'' Prime Minister Bob Hawke said Thursday, assuring students in Australia they need not worry about their visas lapsing and being deported.

In Beijing, statistics show about 80,000 Chinese now are studying abroad, with half of them in the United States, according to the Returned Student Association.

They were permitted to leave China only after passing competitive examinations. Rules published in 1987 said they had to show they ''love the motherland and cherish socialism.'' Political reliability and family connections - relatives in China to ensure their return - are important.

Abroad, many students hope to keep alive the pro-democracy movement. But distance from the tensions in China has not allayed fears of government reprisals. In several countries, students say they believe they are being monitored and harassed by Chinese authorities.

At Brandeis University near Boston, mathematician Cheng Mo, 26, said he suspected the Chinese government was responsible for taking down posters after a meeting of Chinese students.

In Japan, a Chinese student who asked not to be identified said diplomats had photographed demonstrations outside the Chinese Embassy in Tokyo.

''Although they couldn't possibly identify everyone, many of us are worrying,'' he said.

Another student in Japan, also asking anonymity, said pro-democracy activists have toned down the optimism they felt two weeks ago.

''It looks like the battle will be a long one,'' he said. ''None of us wants to do anything conspicuous. But we will continue to fight. Maybe publish a magazine or something. We won't make any needless sacrifices.''

Some Chinese even want to move to Taiwan, where the mainland's old rulers fled after the communist revolution.

Taiwan's de facto embassy in Tokyo said 200 Chinese students had picked up applications for Taiwanese passports and 20 had submitted them in the last four days.

In London, the Free Chinese Center, which represents the Taiwan government in Britain, has received several dozen applications for citizenship ''and we expect more to come,'' said spokesman Kate Hanniker.

The Taiwanese government announced last week it would relax its rules and issue Taiwan passports to Chinese students who had pariticipated in rallies in other countries supporting the demonstrators in Beijing.

''This is to show our concern for overseas mainland students. We hope our passports will help them complete their studies in foreign countries,'' said Foreign Ministry spokesman Chen Yu-chu in Taipei.

But holding a Taiwan passport will not guarantee permanent residence in Nationalist China, he said, because the country's laws say mainland Chinese must live four years in a free country to be eligible for entrance and residence on the island.

The Taiwanese Education Ministry has proposed offering financial help to mainland Chinese studying in other countries.

Some of the 3,000 Chinese students in Britain have expressed worry that their financing ends this summer, said Dr. Abraham Lue, assistant principal of Kings College in London.

''And so they are worried that if the situation in China prevails and it's hazardous for them to return, then they're going to find it difficult to find funding and to stay on here longer,'' he told the BBC.

Some Chinese students in the United States fear they will be jailed if they return home, said Ding Xueliang, 36, a Harvard University student who was active in the democracy movement in exile.

''We'll continue to speak out,'' Ding said. ''It could cause more trouble, but our moral obligation is to help our friends in China.''

In Denmark, seven Chinese students and two businessmen have applied for asylum since the crackdown in Beijing, said Inge Thomsen, a department head in the Aliens Directorate. She said Danish authorities would be cautious in forcing any Chinese to return to China under the present circumstances.