HONG KONG—A standoff over China’s encroachment on this city’s legal autonomy deepened, with hundreds of police firing tear gas and rubber bullets at protesters, as the financial center’s Beijing-backed government showed no signs of yielding during a second day of widespread demonstrations.

Wednesday’s protest, which followed a mass demonstration by as many as a million people on Sunday, is the biggest outbreak of public unrest in years and comes as the administration of President Xi Jinping of China moves to bring the former...