Soviet Ethnic Unrest Flares in the South : Nationalism: Azerbaijanis call for a vote on secession, and Georgians talk of breaking with Moscow. Armenians are attacked in Baku.

A fresh upsurge of nationalist tension on the Soviet Union’s southern flank confronted President Mikhail S. Gorbachev on Saturday on his return to Moscow after an apparently fruitless bid to halt Lithuania’s slide toward secession.

In Baku, capital of Azerbaijan, nearly half a million people rallied to urge a referendum on whether the republic, which has a strong Muslim tradition and flourishing oil industry, should go for independence.

And in Tbilisi, capital of neighboring Georgia, nationalists demanded that Communist Party leaders come from Moscow and talk to them about how their republic can break away. Activists partially occupied Communist Party and government buildings.

Further complicating the picture was a fresh outbreak of anti-Armenian rioting in Baku, where, according to a local independent journalist, some demonstrators left the independence rally to raid a former Armenian quarter of the city. Initial reports indicated there were at least two dead in what the Tass news agency, quoting the official Azerbaijani press service Azerinform, described as “tragic events” that cost human lives.

The journalist, Nazim Ragimov, said the incidents came after some demonstrators broke away from the Azerbaijani independence rally Saturday when “provocateurs” distributed pamphlets calling for a pogrom against Armenians.

Ragimov said worse violence was prevented by leaders of the Azerbaijani Popular Front, who rushed from the demonstration to argue with the crowds and persuade them to halt their attacks.

Meanwhile, in Lenkoran, near the Iranian border, Azerbaijani nationalists have seized government buildings and say they will stay there until the republic’s territorial dispute with Armenia is resolved.

A spokesman for the Popular Front said by telephone from Lenkoran that his organization had taken over all public buildings, party and police headquarters and the post office.

The latest upheavals in Azerbaijan, which started a week ago when nationalists began tearing down sections of the border fence with Iran, pose an additional problem for Gorbachev, already wrestling with secessionist moves by the Baltic republic of Lithuania.

While the independence movement in the Caucasus is far less advanced than in the Baltic region, a strong nationalist tide in the south has frequently been marked by violence and Moscow has appeared incapable of maintaining order.

Tass said police and Communist Party officials in Baku were working to stabilize the situation there and had made arrests.

Ragimov said he had no immediate information on the nationality of the dead. Very few Armenians remained in Baku after a pogrom against them in the nearby city of Sumgait in February, 1988, he added.

The journalist said the independence rally organized by the increasingly powerful front had approved a resolution calling on the local parliament to hold a referendum on Azerbaijani secession from the Soviet Union.

In Lenkoran, the spokesman for the Popular Front said: “We are not claiming any rights over these organizations. Our aim is to urge them to take measures to solve the Nagorno-Karabakh question.”