MOSCOW (AP) _ A mob stormed a police station and tried to seize weapons in the Uzbek republic's Fergana Valley, where ethnic violence has killed 71 people, official media said today.

More than 600 people have been injured and more than 400 arrested since the unrest began about two weeks ago in the eastern part of the Central Asian republic, official Radio Moscow said.

Thousands of Interior Ministry soldiers have curbed, but not stopped, arson and murder in the area, 1,500 miles southeast of Moscow.

The official Tass news agency reported that in the region's city of Kokand, a crowd of thousands ''stimulated by alcohol and drugs'' stormed a police station Wednesday and tried to take weapons, while another crowd of 600 attacked the transportation department of the Interior Ministry.

The attempts to obtain weapons failed, but so did appeals from Kokand government and party leaders for calm, Tass said. Six people died and more than 90 were injured; 65 houses and more than 20 cars were set ablaze, it said.

''More houses are burning,'' Tass reported today.

In the city of Fergana, which has a population of more than 200,000, shootings and arson attempts continued Wednesday night, Radio Moscow reported.

A dispute between Uzbeks and an ethnic Turk minority led to ''pogroms, arson, beatings and murder, accompanied by harassment and rape in conjunction with insolent marauding, resistance to police and internal security forces,'' Uzbekistan's premier told the government newspaper Izvestia.

The premier, Gayrat Kadyrov, said 141 police officers along with 100 civilians were hospitalized. He said he expected the death toll of 71 to rise as the wounded died and more corpses were found in the ashes of gutted houses.

''Passions are still boiling,'' Izvestia said.

About 9,000 internal security troops have been brought in to quell the unrest, but Tass said the government refrained from bringing in the Red Army.

Tass said law enforcement officers and soldiers in the area have been authorized to use weapons for self-defense.

An Uzbek grass-roots movement, Berlik, appealed today to the Soviet parliament to remedy the miserable living conditions that it said helped give rise to the unrest.

''People in the villages are living on the edge of poverty and subsisting on bread and water because of the monopoly on cotton,'' said the appeal, read over the telephone from Tashkent by the movement's secretary, Gavkhar Normatova.

Activists claim that cotton production quotas imposed on Uzbekistan by Moscow have resulted in neglect of food production and ensuing shortages, and has poisoned the enviromment with intensive use of fertilizers and pesticides.

''There are 1.5 million unemployed in Uzbekistan,'' Normatova said. ''The real reason for this unthinkable slaughter is the economic, political and cultural frustration of the people.''

Kadyrov said more than 10,000 members of the Meskhi-Turk minority involved in the unrest have been evacuated to a military training camp. ''I don't want to oversimplify the situation,'' he said, ''but I have grounds to say we are putting the situation under control.''

The Meskhi Turks were deported from their homeland in Soviet Georgia in 1944 by Josef Stalin and forcibly resettled in the Central Asian republic.

Officials say the violence began on May 23 during a marketplace dispute between a Meskhi Turk and an Uzbek fruit vendor. The unrest since has spread from city to city in the Fergana region.

Over the weekend, more than 400 houses, 116 cars, eight industrial enterprises and some schools and government offices were destroyed, many by arson, Tass said.

Uzbeks and Meshki Turks are traditionally Moslem. The Turkish minority has been pressing its demands to be allowed to return to its ancestral homeland in Georgia.

In Moscow, President Mikhail S. Gorbachev told the Congress of People's Deputies on Wednesday that authorities had the situation in the Fergana Valley under control but that there were still incidents of arson and killings.