Ms Park was forced from office on Friday, after judges unanimously upheld parliament's decision to impeach her over her role in a corruption scandal involving close friend, Choi Soon-sil.
Despite the ruling, she remains inside the presidential compound.
Thousands turned out for rallies in Seoul on Saturday, a day after three people involved in protests died there.
Many were calling for Ms Park's arrest, although a smaller number of her supporters also gathered in nearby streets.