Hundreds of thousands of South Koreans have rallied in Seoul in the sixth straight weekend of protests demanding the resignation of President Park Geun-hye.
Three opposition parties have introduced a bill to parliament seeking the impeachment of Ms Park, saying she has violated the constitution and criminal law by abusing her power.
The bill, signed by 171 members of the 300-seat unicameral assembly, said Ms Park had violated the constitution and criminal law by abusing her power in the influence-peddling scandal.
Protesters marching to within 100m of the presidential Blue House called on Ms Park to step down immediately, rejecting her third public apology and request to parliament to decide when and how she should quit.
"It's a national disgrace that she's still in that position. She should have already stepped down," said Kim Jae-hwa, a 43-year-old mother from Seoul, who attended the rally with two adolescent daughters.
One held a red sign reading "Arrest Park Geun-hye".
"I felt it was important for their education to see what democracy is," Ms Kim added.
Ms Park is accused of colluding with a friend, Choi Soon-sil, who has been accused of abuse of power, to put undue pressure on conglomerates to contribute money to foundations that were set up to promote her policy initiatives.
Ms Park has denied wrongdoing but has apologised to the nation.
The three opposition parties said on Friday they would hold a parliamentary impeachment vote on Ms Park on 9 December. A bill once introduced is reviewed by the parliament secretariat, a formality, before it can be reported to the plenary session.
The bill was expected to go to the session on Thursday.
The three opposition parties have enough members to bring the impeachment but will need 28 members from Ms Park's Saenuri Party to bring the vote to the two thirds majority required to pass the bill.
It was not clear whether enough Saenuri members would support the vote.
Rally organisers estimated 500,000 people participated in Saturday's protest, while police declined to estimate the crowd's size but said about 20,000 police personnel were on hand.
In contrast to protest rallies in the past that sometimes involved clashes with police, the weekend demonstrations have been peaceful, resembling large public fairs.
A mix of young and old took part on Saturday, many checking their smartphones for the whereabouts of friends, some in long lines for bathrooms and stalls selling electric candles, selfie sticks, snacks and heating pads.