PRAGUE—With its foggily lit Gothic alleyways, Prague has long had the image of a hotbed of international espionage. A recent report by the Czech Republic’s national intelligence agency, the Security Information Service, or BIS, does little to dispel that narrative.

It cautions that Russia and China are steadily increasing their efforts to sow division and win influence in this small country in the heart of Eastern Europe, which is a member of the European Union and NATO. Both Moscow and Beijing are widely suspected of seeking to provoke instability across the West, but in few countries are these tussles playing out more openly than in the Czech Republic. ...