The parade march for the "liberation" of the Baltic republics in 1940 was a cheerful jazz tune and there was more patriotic jazz music released during the war.

American music has already been used in media about «the plight of the negro» back in the 1930s.

The clampdown came during the campaign against «rootless cosmopolitanism» after the war. The fate of a Jewish jazzman who fled Germany for the USSR was made into a documentary film called «the Jazzman from the Gulag». Here you can have an excerpt in English and here is the entire thing in Russian.