U.S., British and Dutch authorities jointly accused Russia of a widespread hacking campaign, describing on Thursday a persistent effort by the Kremlin to attack agencies that exposed Moscow’s alleged misdeeds, including doping by its athletes and the poisoning of a former Russian officer in Britain.

The Dutch government said early Thursday its intelligence services had disrupted a Russian plot to hack into the Organization for the Prohibition of Chemical Weapons in The Hague in April. Authorities said Russian officers tried...