Ms Park's presidency has been rocked by allegations that a close friend used her ties to the leader to meddle in state affairs and wield improper influence.
Prosecutors have indicted her friend, Choi Soon-sil, and are seeking to question the President about her role in the scandal.
Organisers said 800,000 people had gathered early on Saturday evening and expected a total of 1.5 million people to join by the end of the night.
Police declined to give an estimate of the crowd size but said 25,000 personnel had been dispatched to police the protest.
The protests have remained peaceful, and were marked by huge candle-lit rallies where activists and rock bands have entertained a diverse crowd of students, office workers, and young families.
"I was watching the news and thought this cannot go on — people really want her to step down but she hasn't," said 45-year-old Kwak Bo-youn, one of the protesters.
"This is the second time for me to the protests, but the first time for my husband and kids."
Earlier in the day, a large group of demonstrators marched to within 200 metres of the presidential palace, where Ms Park lives, but a court appeal to allow protesters to remain there after dark was rejected.