More than two million South Koreans hit the streets demanding the ouster of President Park Geun-hye, the largest-ever mass gathering in the country's history.

It was the sixth straight weekend that massive crowds gathered in the capital, Seoul, to force Park out of office, as the country's three opposition parties introduced an impeachment bill in parliament.

Protest organisers told Al Jazeera the number of demonstrators swelled to 1.7 million as of 13:00 GMT on Saturday, surpassing last weekend's 1.5 million people.

Al Jazeera's Harry Fawcett, reporting from Seoul, quoted officials as saying as many as 500,000 more people also protested in other parts of the country. 

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Police estimated the turnout in Seoul at 320,000, though the crowd appeared to be much larger, according to The Associated Press news agency.

Fawcett said the protesters "don't seem satisfied" by Park's offer on Tuesday, to voluntarily leave office by April and hold an early presidential election in June.

Opposition parliament members have criticised Park's overture, saying it was a stalling ploy aimed at luring back members of her party who supported her impeachment.

Opposition parties registered an impeachment motion, which could be voted on as early as next Friday.

The motion, which had the support of 171 opposition and independent legislators, accuses Park of violating the constitution and undermining democracy by allowing her longtime friend, Choi Soon-sil, to interfere in state affairs, and letting senior presidential aides help Choi extort from companies.

It also accuses Park of other crimes, including abuse of authority, coercion and bribery.

Police allowed protesters to advance to a narrow alley about 100 metres away from the presidential palace [EPA]

Squabbling in parliament

The scandal has sparked mass protests each Saturday in downtown Seoul. 

Demonstrators advanced to a narrow alley about 100 metres away from the presidential palace grounds, an area police did not previously permit them to enter.

Some of the protesters, 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 for Park's arrest, not just her resignation.

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

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Protesters are also trying to pressure parliament members, 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 on Tuesday to resign, leaving legislators squabbling over timing.

Some anti-Park parliament members from her own ruling party have called for her to announce by Wednesday, that she will step down voluntarily in April.

It remains uncertain whether those parliament members, numbering between 30 and 40, will back the impeachment bill if she makes the commitment to resign, Al Jazeera's Fawcett said.

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Without their support, there would not be sufficient numbers, to pass the impeachment motion.

Park's confidante, Choi, now faces charges for meddling in government affairs and, in a first for a sitting South Korean president, Park had earlier been named a "suspect" by prosecutors.

As president, Park cannot be charged with a criminal offence, except insurrection or treason, but she would lose that immunity once she steps down.

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Source: Al Jazeera News and Agencies