HONG KONG—Clashes between protesters and police became more violent and widespread and activists’ calls for a citywide strike shut down parts of Hong Kong on Monday, escalating a crisis as the city’s top official refused to make concessions.

Police and gangs of men wielding bamboo sticks and other weapons engaged in pitched battles with protesters in many districts of Hong Kong. The day’s protests, unlike most in nearly two months of unrest, started on a weekday morning, an effort by protesters to bring working life in the...