South Korean President Park Geun-hye is facing mounting pressure to step down as hundreds of thousands of demonstrators march in the capital to protest allegations that she let a friend meddle in state affairs.

Saturday's rally in downtown Seoul was the largest so far in a crisis engulfing Park, 64, and organizers said some 850,000 people packed streets running through the city centre including a 12-lane thoroughfare. Police estimated the crowd at 260,000.

Students, families including young couples pushing strollers and protesters in wheelchairs were among the crowd during the peaceful march, which contrasted with the violence of some previous rallies dominated by militant unions and civic groups that clashed with police.

One man travelled seven hours from the southern town of Gimhae to join the rally demanding Park step down a year before her mandate is due to end.

“Park Geun-hye! Today! Step down! Immediately! Step down! Now!” protesters chanted a few hundred metres (yards) from the presidential Blue House.

“I'm here so that this country will be a better place for my daughters,” said Park Min-hee, 34, a housewife who was at the rally with her two young daughters and her husband's parents. “Park Geun-hye did wrong. She must step down right now.”

It was the third weekend protest rally since Park's first public apology on Oct. 25 when she admitted she had sought the advice of her friend, Choi Soon-sil.

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Park's acknowledgement only served to fuel public anger and suspicion over the secret confidant, who apparently held no official government position.

Another apology by Park and an offer to work with the parliamentary opposition to form a new cabinet and relinquish some power also failed to quell the crisis, prompting opponents to say she did not grasp its severity.

Park has dismissed some of her most senior and closest advisers, and former aides have been arrested on charges of abuse of power. Choi, the friend who is believed to have been acquainted with the president since the 1970s, has been charged with abuse of power and fraud.

Members of main opposition parties joined Saturday's rally, suggesting there is growing support in parliament for action to remove her from power, although there was no formal move yet to launch impeachment proceedings.

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No South Korean president has ever failed to finish their five-year term.

Park's approval rating has dropped to five percent for a second week, according to a poll conducted by Gallup Korea and released on Friday, the lowest number for a South Korean president since such polling began under democratically elected leaders in 1988.

Gallup Korea, based in Seoul, is not affiliated with U.S.-based Gallup, Inc, the American firm said.

Park is the daughter of Park Chung-hee who took power in a 1961 military coup and ruled until he was assassinated by his disgruntled spy chief in 1979, five years after his wife was shot dead in the head by a killer who meant to shoot him.