SEOUL, South Korea — Hundreds of thousands of South Koreans filled central Seoul on Saturday to demand President Park Geun-hye’s resignation, in what appeared to be the largest turnout yet in a series of weekly protests against the embattled leader.

Despite cold weather and the first snow of the season, a crowd that organizers estimated at 1.5 million gathered to denounce Ms. Park, who has been accused by prosecutors of helping a friend commit extortion and is facing the possibility of impeachment within weeks.

The police estimate of the turnout was much lower, at 260,000, but the crowd seemed larger than at an enormous rally in the capital two weeks earlier. It was the fifth consecutive Saturday marked by a large protest against the president.

The demonstrations have been peaceful and almost festive. Street vendors sold candles, mattresses and hot snacks on Saturday, and a few roadside shops gave protesters free coffee. Buddhist monks beat wooden gongs as they marched. Mothers showed up with children, or with pet dogs wrapped in padded vests, and young couples bundled in winter coats sang along as loudspeakers blared catchy tunes calling for Ms. Park’s ouster.