Google on Friday said it plans to give advertisers more control over where their ads appear online after major clients in the U.K. withdrew their spots because some ads ran before extremist videos on its YouTube site.

Tensions between Google, the world’s biggest advertising platform, and its advertisers have increased over the past several days following a report showing ads by the British government and several companies—including French cosmetics giant L’Oréal SA and British grocery chain J Sainsbury PLC—appeared before...