Organisers said the mass rally would march on the Constitutional Court whose nine justices are considering the validity of the impeachment bill passed by the national assembly more than a week ago.
The court has 180 days to make a ruling, but the protesters are pressing for a swift judgement.
Although Park has been stripped of her substantial executive powers, she is allowed to retain the title of president and continue to live in the presidential Blue House while the court deliberates.
But Park still has her supporters, many of them elderly voters who remain steadfast admirers of her father, the late military dictator Park Chung-Hee -- credited as the architect of the South's economic transformation but vilified as an authoritarian rights abuser.
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Several thousand Park loyalists attended their own rally near the court earlier in the day to demand the impeachment bill be thrown out.
Waving national flags and clutching red roses they carried banners denouncing the anti-Park protests as a leftist conspiracy.
Yesterday, Park's legal team formally submitted a 24-page rebuttal of the impeachment charges to the court, arguing that they had no legal basis.
Park was impeached on numerous counts of constitutional and criminal violations ranging from a failure to protect people's lives to bribery and abuse of power.
Most of the charges stemmed from an investigation into a scandal involving the president's long-time friend, Choi Soon-Sil, who is currently awaiting trial for fraud and embezzlement.
Prosecutors named Park a suspect in the case -- a first for a sitting president -- saying she colluded in Choi's efforts to strong-arm donations from large companies worth tens of millions of dollars.
The National Assembly has played its part, but the country now faces a lengthy period of uncertainty at a time of slowing economic growth and elevated military tensions with nuclear-armed North Korea.