MOSCOW (AP) _ Flags flew at half-staff and festivities were canceled Monday in the Soviet Republic of Kirghizia to mourn the 116 people killed in a week of ethnic clashes in Central Asia, the Tass news agency reported.

The official news agency and Soviet television said the situation in Central Asia had calmed following clashes between Uzbeks and Kirghiz that broke out after a land dispute.

''A trend toward the stabilization of the situation in the republic's southern region has become apparent,'' Tass said, quoting the republic's Interior Ministry.

In Osh, a city near Kirghizia's border with Uzbekistan, shops reopened and public transport was returning to normal, Tass said.

The news agency said 116 people died, 468 were wounded and at least 500 acts of arson were committed in the week of violence.

In memory of the dead, Tass said, ''flags are flying at half-mast and all recreational and entertainment activities have been suspended.''

Kirghizia's capital of Frunze was calm Monday as television and radio broadcast somber music in memory of the dead, said Albert Bogdanov, a journalist with the Kirtag news agency.

On Sunday, students trying to organize rallies in Frunze's main square were turned back by Interior Ministry troops and police, said Ivan Pavlov, a party official in the capital.

Rallies in Frunze last week turned into demonstrations against the republic's leaders with thousands of students demanding their resignations and calling on residents to go to Osh and join the battle against the Uzbeks.

Officials from the Communist Party and the government visited student and worker dormitories Sunday morning to talk them out of holding rallies, Pavlov said.

Armored personnel carriers Monday continued to patrol the main streets of Frunze in districts where trouble had broken out earlier, Bogdanov said in a telephone interview.

The bloodshed was the latest ethnic violence to trouble the government of Soviet President Mikhail S. Gorbachev. Nationalities in various republics have used the looser atmosphere under Gorbachev's reform initiatives to vent their frustrations over political and economic woes.

The violence started when Uzbeks, who make up one-third of the population, discovered that Kirghiz were being given land for housing, which is critically short in the densely populated and poor regions of Central Asia.

The fighting spread to districts around Osh, and thousands of troops were sent in to reinforce the local police. Soviet troops sealed off the border to prevent thousands of Uzbeks from crossing into Kirghizia to join the battle.