HONG KONG — Hong Kong was a city on edge on Monday following escalating violence, in which one demonstrator was shot point blank by a police officer and one man was doused with a flammable liquid and set on fire after he scolded protesters.

At nightfall, both men were fighting for their lives in a city seething with resentments.

Protesters have voiced outrage at police officers they see as increasingly resorting to force, and at a government they say has allowed them to act with impunity. Government supporters are embittered over the protesters themselves turning to violence and the damage it has done to their city.

Months of unrest have thrown the Chinese territory into its worst political crisis in decades, and if Monday was any indication, there is no end in sight.

Carrie Lam, the city’s embattled chief executive, said the mayhem could “take Hong Kong to the road of ruin” and denounced those who had set the man on fire as “enemies of the people.”