People beat drums and chanted "Park get out now" as they walked towards the presidential Blue House that had been cordoned off by thousands of police deployed in the South Korean capital.
By late afternoon 350,000 protesters had joined the march, organisers said. They expect up to 1.5 million to take part in the demonstration, with another half a million in provincial cities.
Police put the figure at 140,000 participants in Seoul.
Parents and their children, university students and Buddhist monks were among those protesting for the fifth straight weekend as Park comes under intensifying pressure to step down.
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The largely peaceful rallies have been growing in size over the past month, attracting an estimated one million people two weeks ago, and are among the largest seen in South Korea since the pro-democracy protests of the 1980s.
Park has issued public apologies over the influence-peddling scandal involving her long-time confidante Choi Soon-Sil, who has been arrested for fraud and abuse of power, but has defied repeated calls to resign.
The 60-year-old allegedly leveraged her relationship with Park to coerce donations from conglomerates, including SK, Lotte and Samsung, to non-profit foundations which she set up and used for personal gain.
Park has promised to submit herself to an expanding probe by prosecutors, as well as a separate investigation by an independent special prosecutor to be appointed by parliament.
Nevertheless her approval ratings have plunged to a record low for a sitting president as top advisers and some of South Korea's most powerful companies are caught up in the ever- widening scandal.
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