SEOUL, South Korea — Rallying for the sixth straight weekend in what has become perhaps South Korea's biggest protest movement ever, hundreds of thousands of demonstrators in Seoul got the closest yet Saturday to the president they desperately want removed.

Protesters gather at a rally calling for South Korean President Park Geun-hye to step down in Seoul, South Korea, on Dec. 3, 2016. AP

The demonstration came hours after lawmakers formally launched an attempt to impeach President Park Geun-hye and set up a floor vote for as early as next Friday. State prosecutors accuse Park of helping a close confidante extort money and favors from large companies and manipulate state affairs.

The scandal has sparked mass protests each Saturday in downtown Seoul. In the latest demonstration, the protesters advanced to a narrow alley about 100 meters (yards) away from the presidential palace grounds, an area police didn't previously permit them to enter.

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Police estimated the turnout at 320,000, making it the biggest anti-Park rally so far, though the crowd appeared to be much larger. Protest organizers estimated the crowd at 1.7 million.

Some of the demonstrators, led by the relatives of a 2014 ferry disaster that killed more than 300 people, mostly teenagers on a school trip, jammed the alley near the presidential office, shouting for hours to demand Park's arrest, not just her resignation.

Some protesters angrily threw flowers at police who had created tight perimeters around the street, and demanded that the officers get out of the way.

"We not once were allowed on this street ... I have long dreamed of the day I stand here with citizens," said Jeon Myeon-seon, one of the parents of the teenagers who died in the ferry disaster, which was partially blamed on government incompetence and corruption. "We will continue to join this fight with our fellow citizens until the full truth is out on how this government defrauded its people."

Protesters gather and occupy major streets in the city center for a rally against South Korean President Park Geun-hye on December 3, 2016 in Seoul, South Korea. Chung Sung-Jun / Getty Images

Thousands also rallied near the National Assembly to pressure political parties, including Park's conservative ruling party, to vote for her impeachment next week.

Opposition parties controlling South Korea's parliament had earlier planned to call for a vote this past week, but were thrown off after Park made a conditional offer Tuesday to leave office, which left them squabbling over timing.

Park's overture has also caused cracks among dissenters in her conservative ruling party who had earlier backed her impeachment, an alarming development for opposition parties, which don't have enough votes to push through the impeachment motion themselves.

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"I am full of anger, but also worried," said Ray Kim, an out-of-towner who participated in the Seoul protests for the second consecutive week. "It would leave a terrible historical example if millions protested for weeks against a crime-committing president but she was able to shake it off."

Opposition parties waited until after the end of the week's plenary session to register an impeachment motion at 4:10 a.m. Saturday. It means the vote will take place as early as next Friday.

Some anti-Park lawmakers in the ruling party have called for Park to announce by Wednesday that she will step down voluntarily in April. It's uncertain whether they will back the impeachment bill if she does.

Park said Tuesday that she would leave office if parliament comes up with a stable power transfer plan, though she didn't provide a timeline. Opposition lawmakers criticized the overture, saying it was a stalling ploy aimed at luring back members of her party who supported impeachment.