HONG KONG—Tens of thousands of protesters poured onto Hong Kong’s streets Sunday, with the fiercest battles in weeks breaking out as demonstrators faced off with police and shouted anti-party slogans ahead of Tuesday’s 70th anniversary of the founding of Communist China.

The protesters had planned to march to the government headquarters in the center of the city under the theme “Global Anti-Totalitarianism Rally.” The police broke up the march at about 4 p.m., an hour or so after it began, engaging the protesters in urban...