WASHINGTON—U.S. officials are increasingly confident that the hacker Guccifer 2.0 is part of a network of individuals and groups kept at arm’s length by Russia to mask its involvement in cyberintrusions such as the theft of thousands of Democratic Party documents, according to people familiar with the matter.

While the hacker denies working on behalf of the Russian government, U.S. officials and independent security experts say the syndicate is one of the most striking elements of what looks like an intensifying Russian campaign...