Estonia and Latvia, the most Westward-looking Soviet republics, have voiced radical demands to next week's Communist Party conference that they be given virtual control of their own affairs.

A published platform for the 32 delegates from Estonia and a letter signed by hundreds of Latvian intellectuals to the national conference demand the two Baltic republics control their own finances, ecological policy, culture, education, media and foreign affairs.Both documents also demand the right to control migration to their republics, where ethnic Estonians and Latvians are now in the minority, and to strengthen the place of their indigenous languages in their schooling and arts.

The demands are the most radical from the Soviet Union's 15-republics since Mikhail S. Gorbachev launched his liberalization campaign, which has given rise to outbursts of national feeling.

Public protests and media articles in recent months in Estonia, Latvia and the third Baltic repbulic, Lithuania, suggest the proposals to the 5,000 delegates of the party conference opening June 28 have strong popular backing.

Radio Moscow reported Wednesday that a crowd of 100,000 people turned out in Estonia to see the republic's 32 delegates off to the conference.

Both their platform and the even more radical demands of the Latvian intellectuals were published in state-run republican media in the past two weeks, ensuring a broad audience is familiar with the proposals.

According to the newspaper Soviet Latvia of June 11, the Latvians demanded "effective sovereignty" over their own resources and treatment of Latvia as a "sovereign national state" with the right to its own membership in the United nations and other international organization and its own team at the Olympic Games.

The Soviet Union annexed the Baltic republic in 1940.

In the 30-page proposals to next week's conference, there is scant mention of ethnic questions that have erupted into violence that has killed at least 34 people in the southern Soviet Union.

The republics of Armenia and Azerbaijan are at loggerheads over the fate of the mainly Armenian enclave of Nagorno-Karabakh, which was incorporated into Azerbaijan in 1923.

Both Baltic demands stopped short of calling for secession from the Soviet Union, which is sometimes demanded by dissident groups and emigres, but made clear they want much more genuine autonomy from Moscow.