Violence in Hong Kong's anti-government protests is becoming more serious but the government is confident it can handle the crisis itself, the embattled leader of the former British colony said on Tuesday.

Carrie Lam was speaking in public for the first time since demonstrations escalated on Sunday, when police fired water cannons and volleys of tear gas in running battles with protesters, who threw bricks and petrol bombs.

The Chinese-ruled city is grappling with its biggest political crisis since its handover to Beijing in 1997 and Communist Party authorities have sent a clear warning that forceful intervention is possible to quell the violence.