As far as I know, it wasn't a program structured with a brand image in the same way as the Peace Corps, but the USSR was certainly engaged in the business of sending its citizens to perform service to underdeveloped countries on the Cold War periphery in hopes of projecting "soft power" and instilling a sympathetic sentiment of the USSR and communism in these places. Moreover, the USSR was doing this before the US, which was a source of concern for Kennedy, who was worried about the growing influence of the USSR and communism in the "Third World" in the wake of a period of generally inflexible, power-oriented foreign policy under Eisenhower, which had left little room to prioritize softer diplomatic strategies that would paint a positive image of the US and its ideology abroad.

Indeed, in a campaign speech Kennedy gave on the subject of America's lackluster cultural diplomacy skills just before his election in 1960, he directly referenced this fact as among the very inspirations for his idea that would later become the Peace Corps.

We are going to have to have the best Americans we can get to speak for our country abroad. All of us have admired what Dr. Tom Dooley has done in Laos. [Applause.] And others have been discouraged at the examples that we read of the ugly American. And I think that the United States is going to have to do much better in this area if we are going to defend freedom and peace in the 1960's. [Applause.] For the fact of the matter is that out of Moscow and Peiping and Czechoslovakia and Eastern Germany are hundreds of men and women, scientists, physicists, teachers, engineers, doctors, nurses, studying in those institutes, prepared to spend their lives abroad in the service of world communism. A friend of mine visiting the Soviet Union last summer met a young Russian couple studying Swahili and African customs at the Moscow Institute of Languages. They were not language teachers. He was a sanitation engineer and she was a nurse, and they were being prepared to live their lives in Africa as missionaries for world communism.

Source/full transcript of the speech

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