And elections in 1993 (after the dissolution of parliament) were won by Zhirinovsky's party, communists were only 3rd. US never supported Zhirinovsky and he wasn't a communist.
I don't see how US could be blamed for anything that happened in 1993 because they were really trying to stop the crisis, but far-right nationalists (like Barkashov and Makashov) started military actions, like mayor's office assault and TV building attack.
This is not a "returning to power ... through elections" for sure.