SEOUL, JUNE 12 -- Street battles between police and antigovernment demonstrators continued for a third day today, with officials showing signs of concern over the unusually long duration of the disturbances.

Crowds of protesters, most of them apparently students, shouted, "Down with military dictatorship" and pelted police with stones late into the night over a wide area of the city.

Most appeared to have come out in support of about 300 student protesters who have been besieged by riot police at Seoul's Roman Catholic cathedral since Wednesday night. There was no violence at the church itself.

Police tactics of tear-gas barrages followed by close-order sweeps normally end such protests fairly quickly. Now, however, demonstrators are treating them as little more than a nuisance.

Dozens of times today, the police attacked this way, only to see the demonstrators melt away and within a few minutes form up again on the next block. Chants of "Down with military dictatorship" would arise and, in a few minutes, fighting would resume.

As happened on the first day of protests Wednesday, a police unit of about 30 men was overrun by demonstrators, beaten and stripped of helmets and equipment.

In most places, the demonstrators numbered fewer than 100. Here and there, passers-by joined in. Witnesses said that at lunch time in a commercial district near the church, a crowd of office workers argued with police and ignored orders to disperse.

Public anger appears to have been stoked by indiscriminate use of tear gas. Fired from armored cars, rifles and grenades, it has left hundreds of thousands, possibly millions, choking in their homes and work places.

Students on several campuses in Seoul, meanwhile, staged support rallies. At Yonsei University, an estimated 4,000 fought police, then staged a sit-on at the university's gate.

In another embarrassing development for the government, play in an international soccer match, the President's Cup, was stopped for a second time this week when gas swept over a field in Pusan.

Seoul is to host the Summer Olympics in 1988. Critics have asked whether it can guarantee safe playing conditions if the political system is in turmoil.

Culture and Information Minister Lee Woong Hee said in a statement that the protests were intended to "induce a violent revolution by undermining law and order." He said the government "will resolutely and sternly deal with any segment of society or any group of individuals that breaches the law and creates social chaos."

The continuing sanctuary of the students at the cathedral, he said, "is almost certain to lead to unforeseeable confusion in the basic national order, if it is left unchecked." So far, police have stayed out of the church but said they will arrest the students.

One National Assembly member from the ruling party said this morning before the disturbances flared again that the government would be worried if the demonstrations got bigger.