They want to carve out their own autonomous region, loyal to Moscow instead of Kishinev, the Moldavian capital.
The militants who attacked the frontier checkpoints Wednesday also threatened to go to the Moldavian capital of Kishinev "to restore order," according to Tass.
Konstantin Rabu, a member of the Moldavian People's Front, said in a telephone interview from the Moldavian capital of Kishinev that the volunteers were unarmed and would try to end the Gagauz independence drive peacefully.
The Moldavian Interior Ministry, reached by telephone in the republic capital, Kishinev, declined comment on today's unrest.
In Kishinev, capital of the republic of Moldavia, youths boycotted a rally after student activists were refused their own column in that city's parade, Izvestia said.
Rozhgo said the People's Front would hold a large rally Sunday in central Kishinev to press its demands.
The movement fielded candidates for each of the 65 districts in Kishinev.
The military part of the parade in its capital, Kishinev, was canceled.
Around Kishinev, capital of this republic on the Romanian border, viewers watched the session on television in both Russian and Moldavian, a Romanian dialect.
The Supreme Soviet session addressing the law opened Tuesday, and several thousand people, some carrying red-yellow-and-blue Moldavian banners, gathered after the debate in downtown Kishinev to show support for the People's Front.
Tass quoted First Deputy Interior Minister Konstantin Antoch as saying Kishinev police were on alert, but "proved ineffective and somewhat late" in stopping the rampage.
Thousands of demonstrators with signs reading "Down with the Government" gathered March 19 in Kishinev, the tiny western republic's capital, the Communist Party daily said.
They also threatened to go to Kishinev "to restore order," according to Tass.