Ms Park is accused of allowing her friend, Choi Soon-sil, to manipulate power from behind the scenes.
The president has apologised twice on national television, but has so far resisted calls to resign.
Organisers said 1.3 million had gathered in capital Seoul on Saturday night, 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.
