South Korea is seeing what is thought to be the largest protests so far demanding President Park Geun-hye steps down.
Park Geun-hye is accused of allowing her friend, Choi Soon-sil, to manipulate power from behind the scenes.
She has apologized twice on national TV, but has so far resisted calls to resign.
According to protest organizers, 1.3 million people had gathered Seoul on November 26, despite cold weather and snow.
They expect another half a million protesters to turn out in other regions.
However, police put the turnout at about 260,000. About 25,000 officers were being deployed in the capital, local media said.
The protests, which began five weeks ago, are the largest in South Korea since pro-democracy demonstrations of the 1980s.
Those attending on November 26 came from a cross-section of South Korean society, with farmers, Buddhist monks and university students all involved.
Park Geun-hye, whose approval rating has dropped to 5%, apologized earlier this month for putting “too much faith in a personal relationship”, and has pledged to co-operate in an official investigation into the scandal.
South Korea’s constitution does not allow a sitting president to be prosecuted, and Park Geun-hye has 15 months left in her term.
Now that prosecutors have directly linked Park Geun-hye to the scandal, it is possible she could be impeached for breaking the law.
Prosecutors are expected to bring charges against Choi Soon-sil, along with two former presidential aides. She was arrested earlier this month.
Choi Soon-sil is accused of trying to extort huge sums of money from South Korean companies, and suspected of using her friendship with President Park Geun-hye to solicit business donations for a non-profit fund she controlled.