It was literal American policy to pressure other countries to do so. I mean an open one - not a secret, but something American politicians were proud about. It was seen as a good thing by them and by the voters.
Soviet Union did not had all drug war in this sense.
Drug scene in Soviet Union was massively different then the one in the West. A lot of western drugs were not available and came only with the fall of the Union. The actual issues were alcohol and sniffing. The actual drug scene was something that came with opening of the borders and society needed to adjust.
Soviet Union doing something is not proof that American policy was not what I said. Soviet Union did stuff for own reasons. They did not forbid just drugs either, they forbid half the things existing outside of their borders.