SEOUL, JUNE 25 -- The soccer match between teams from South Korea and Egypt had been in progress for barely 30 minutes before the acrid fumes of tear gas entered the stadium in the southern port city of Masan. Riot police were firing the gas at students demonstrating near the stadium.

The players stopped the game, covering their faces with their T-shirts. Within minutes, 30,000 fans, choking on the gas, were streaming out of the stadium.

Two days later, it happened again in the city of Pusan, this time during a match between the Korean and U.S. teams.

The interrupted soccer games, which took place at the outset of violent political protests in the streets earlier this month, have prompted rumblings abroad that Seoul is perhaps incapable of hosting next year's Summer Olympics.

Los Angeles Mayor Tom Bradley and West Berlin Mayor Eberhard Diepgen have offered their cities as alternative hosts if the venue is changed. New York City and Indianapolis, where the Pan American Games will be held this summer, have also proposed to host the games if Seoul is forced to drop out.

The suggestion that the Olympics may be moved elsewhere has mortified government officials and many ordinary citizens as well. Few things are more important to South Korea than playing host to the games its newspapers call "a great festival of mankind" and that the Korean people proudly see as a showcase for their entry into the ranks of leading industrial nations.

For that reason, the Olympics are becoming an increasingly critical factor as President Chun Doo Hwan tries to find a way to solve the current political crisis. He must somehow restore order and confidence that the games will not be disrupted by political violence, yet he must also avoid the use of brute force that would leave his government open to charges of heavy-handed tactics unfit for an Olympic host.

Two major leaders of the opposition have said the Olympics could be jeopardized if Chun refuses to give way to their demands for a democratically elected government. Kim Dae Jung, who was freed briefly from house arrest yesterday, said only the achievement of democracy could guarantee the games' success.

After seeing Chun to explore ways to defuse the crisis, Kim Young Sam told reporters that without a democratically elected government "the Olympic Games will be very, very difficult, almost impossible to hold."

{Kim Ock Jin, secretary general of the Seoul Olympic Committee, told the general secretaries of the European Olympic Committees, meeting Thursday in Nicosia, Cyprus, that the unrest was a political problem that will "be fully settled soon" and had not affected preparation for the games, The Associated Press reported.}

For South Korea, hosting the games holds greater symbolic importance than overseeing an international sporting event. It is nothing less than a test of national fiber.

The South Korean press describes the games as the "pride and joy" of the Korean people. Hosting them, newspapers trumpet, will prove to the world that South Korea is prepared to join the ranks of advanced industrialized countries.

The precedent often cited here is the 1964 Olympics held in Japan, which illustrated that country's postwar recovery and provided a substantial economic and psychological boost for Japan's further development into a mature industrial democracy.

The games are seen by officials here as further proof to the world that they, not the communist authorities in North Korea, are the legitimate government of this divided nation. North Korea has demanded rights to cohost the games. The South has offered it all or part of four separate sporting events, but talks have deadlocked because Pyongyang has demanded more events.

Seoul has spent five years and billions of dollars building facilities and beautifying the city to prepare for the games, which are scheduled to take place from Sept. 17 to Oct. 5, 1988.

Officials from the International Olympic Committee have said they are watching the political situation, but are not planning to shift the games to another site. On Sunday, the committee's vice president said the IOC would decide three months before the starting day about withdrawing from Seoul, if political turmoil continues.

One committee member has said the only provision that would allow for switching sites is an act of war.

Suggestions that South Korea may not be able to handle the political turmoil have been viewed here as an affront to national pride.

"It is shameful that some foreign countries, citing Korea's political unrest, are trying to host the next Olympics in behalf of us," Park Seh Jik, president of the Seoul Olympic Organizing Committee, said Tuesday.