HONG KONG—Police fired water cannons and tear gas to disperse protesters besieging the city’s government headquarters, as tens of thousands took to the streets in defiance of a police ban on antigovernment demonstrations.

Violence flared in the Admiralty area late Saturday afternoon after crowds occupied major roads in processions that stretched for miles through the city. In other districts, people of all ages held umbrellas in drizzling rain, chanting for freedom as social unrest stretched into a 13th weekend.

By about 5:30 p.m., police fired multiple volleys of tear gas to disperse the crowds, followed by jets of water from water cannons—some with blue dye to stain protesters. Protesters, some clad in head-to-toe black outfits, with helmets and shields, tossed rounds back at police and flashed laser beams in response. Some threw tear-gas canisters into the complex that serves as the Hong Kong headquarters of China’s People’s Liberation Army, which is next to the Hong Kong government building.