Park was impeached by parliament last month over an influence-peddling scandal and the Constitutional Court now has to decide whether to confirm the impeachment.
The corruption scandal has brought huge numbers of protesters onto the streets every week demanding Park's removal and she is also under fire over her response to the Sewol ferry accident in 2014.
"Park step down, salvage the Sewol," the protesters, estimated to number half a million by organisers, chanted as they marched toward the presidential Blue House, the prime minister's office and the Constitutional Court.
Unconfirmed media reports have suggested a wide range of theories regarding Park's whereabouts, including a romantic liaison, participation in a shamanistic ritual, cosmetic surgery or a 90-minute haircut.
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The protesters also urged the government to speed up its efforts to salvage the ship to determine the exact cause of the disaster.
Regarding the corruption case, Park has repeatedly denied accusations she colluded with a longtime friend, Choi Soon-Il, to strong-arm donations worth tens of millions of dollars from top firms which were then funnelled to dubious foundations.
Waving national flags and chanting military songs, the protesters dismissed the impeachment move as a conspiracy spawned by "pro-North Korean" leftists seeking to topple the conservative government.