SEOUL, South Korea (AP) _ Thousands of students throughout the country chanted ''Down with dictatorship 3/8'' and fought police Thursday in protest of President Chun Doo- hwan's decision to stop debate on constitutional change.

News reports said the demonstrations involved 13,000 students at 24 universities in Seoul and other cities.

There were no over-all reports on arrests and casualties, but witnesses reported at least 10 demonstrators injured in Seoul.

Chun declared last week that no changes will be made in the constitution until his successor is chosen by an electoral college in February. The opposition has demanded an amendment providing for direct presidential elections before his term ends.

The government says stern action will be taken against anyone who attempts to foment ''social chaos'' and endanger the 1988 Summer Olympics, of which South Korea is host.

Prosecutor-General Suh Dong-kwon met with his senior officials Thursday and ordered a special crackdown on political dissent.

About 600 students at Sogang University in Seoul hurled rocks and fire bombs at riot police Thursday and the officers fired tear gas in response, witnesses reported. They said at least 10 students were injured, including two hit in the head by tear gas canisters.

Students chanting slogans against the Chun government and the United States tried repeatedly to break through police lines, according to the reports. The national newspaper Chosun Ilbo said there were at least nine arrests.

Campus sources and newspaper reports said students demonstrated at eight Seoul universities and 16 schools in other cities, with all protests confined to campuses. There was no immediate comment from police.

Anti-American feeling was strong at Korea University in Seoul, where students flung stones and eggs at Park Bo-hi, a confidant of the Rev. Sun Myung Moon, leader of the U.S.-based Unification Church.

Park, 58, was unhurt but at least one of his bodyguards suffered a head injury. The retired army officer was a virtual hostage for more than an hour after trying to deliver a speech on ''Korean Unification.''

About 2,000 students interrupted Park's presentation and forced him out of the auditorium. Witnesses said the barrage of stones began as he was about to speak and students shouted: ''You pro-American flunky, get out 3/8''

One student said later: ''We don't like the Unification Church because it is close to the government.''

South Korea's 120,000 national police were put on alert Thursday in case of demonstrations. A spokesman said the readiness will continue through the 27th anniversary Sunday of a student uprising April 19, 1960, that brought down the government of President Syngman Rhee.

South Korean students, traditionally critical of the government, usually mark the day with large demonstrations on campuses and in the streets.

Police said they searched facilities at 52 universities and colleges throughout the country overnight, seizing leaflets and firebombs. No arrests were reported.

In a special anti-crime check Wednesday, police detained more than 4,000 people, most said to be involved in non-political crimes.

Constitutional amendments have been a major political issue since early last year, when Chun promised changes in a program of democratic development.

Opposition leaders, demanding direct presidential elections, contend the electoral college system favors those in power.

Chun's ruling Democratic Justice Party proposes a parliamentary-style system with a strong prime minister and figurehead president.

If Chun steps down at the end of his term next February, as he has promised repeatedly, it will be South Korea's first peaceful transfer of power. Chun, a former army general, took over after the assassination of President Park Chung-hee in 1979.