HONG KONG—The arrests of Hong Kong activists, including some of the most prominent figures of the pro-democracy movement, and the ban of a mass rally set the stage for a pivotal weekend showdown between protesters and the city’s authorities, as the confrontation showed no signs of abating.

In a series of arrests Friday, police rounded up at least eight opposition figures, including Joshua Wong and Agnes Chow, who are among the best-known faces from the 2014 Umbrella Movement protests. The arrests—combined with the decision...