MOSCOW — Russia’s communications watchdog was locked in an intensive game of whack-a-mole on Wednesday with Telegram, the popular and highly secure messaging app, as its stuttering attempts to block the service inadvertently knocked out the websites of scores of small businesses.

Alexander Zharov, the head of the watchdog agency, Roskomnadzor, acknowledged that it had obstructed millions of IP addresses in an attempt to shutter Telegram. Roskomnadzor took that step after the company declined to provide encryption information, which would enable the agency to identify users and see the content of messages.

The watchdog agency was granted authority to block the app on Friday by a Moscow court. But the clumsy, unprecedented effort to follow through, which started Monday, caused a widespread outcry after the unintended consequences became apparent.

A member of the band Pussy Riot organized a small public protest. Edward J. Snowden, the former N.S.A. contractor who leaked American surveillance documents and now lives in Russia, expressed support for the company. Even some usually staunch Kremlin supporters called the ban misguided.