The purges came in the midst of the Great Depression, and were not, as the previous post indicates, cause for much concern among most nations. However, the purges did lead to widespread disillusionment with communism among the far left in the United States. Left-wing intellectuals abandoned communism in the wake of the purges (and the Nazi-Soviet pact). The most famous of these intellectuals was probably Robert Oppenheimer.
The world essentially did not respond to Stalin's purges. It was an internal matter in the Soviet Union and no one really cared enough or had the ability to try to do anything about it. The Soviet Union was so closed off at the time that there was really nothing that could be done even if anyone in the world had cared about what happened to communists who happened to get on the wrong side of Stalin.