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.

One such song quoted from South Korea’s Constitution: “The Republic of Korea shall be a democratic republic.”

Prosecutors have identified Ms. Park as a criminal accomplice in the case of Choi Soon-sil, an old friend who has been charged with using her influence to coerce businesses into donating large sums to foundations that Ms. Choi controls. In news reports, Ms. Park has also been accused of letting Ms. Choi wield undue influence in state affairs.

Ms. Park, who cannot be prosecuted while in office, has apologizedtwice to the public over the scandal but has refused to resign as opposition lawmakers, major newspapers and some members of her own party have demanded.

Opposition parties hope to impeach her with the support of some lawmakers from her party. The National Assembly is expected to vote on an impeachment bill by Dec. 9.

No South Korean president has ever been removed from office through impeachment.

On Saturday, some protesters chanted, “Imprison Park Geun-hye!” as they marched toward the presidential Blue House. “Come out and surrender!” they shouted.

Hundreds of buses and thousands of police officers had been deployed to form barriers around the complex. One group of demonstrators was stopped just 200 yards from the presidential compound.

Protesters holding candles marched through central Seoul late into the night. Rock musicians performed on the main thoroughfare, replacing the lyrics of popular songs with phrases that criticized and ridiculed Ms. Park. Some people carried doctored images of Ms. Park in a prison uniform and handcuffed.

On smaller streets, citizens spoke to the crowd from the back of trucks. One teenage girl railed tearfully against Ms. Park for failing to respond effectively to the Sewol ferry disaster in 2014, which left more than 300 people dead, most of them teenagers.

She also criticized the government-written history textbooks that Ms. Park’s administration has said it plans to issue for use in all middle and high schools starting next year.

Protesters accused Ms. Park of trying to take South Korea back to the time when it was ruled by military dictators, including her father, Park Chung-hee, and the practice of shaking down businesses was commonplace.

At one point, at the suggestion of organizers, the protesters all blew out their candles to symbolize the darkness into which, they said, Ms. Park has led the country.

Many protesters said they wanted Ms. Park to be impeached, providing a dramatic end to her tenure.

“What we have seen happening at the Blue House is just like a soap opera,” said Kim Yong-jin, a high school senior. “We just hope that it ends like a soap opera — with poetic justice.”