The street protest came as prosecutors investigate presidential aides and other officials to determine whether they broke the law to allow Park’s friend, Choi Soon-sil, to wield undue influence and gain financially.
Angry Koreans say that Park betrayed public trust and mismanaged the government, and has lost a mandate to lead the country.
Over the past week, the media has been full of increasingly sensational reports regarding Choi, the 60-year-old daughter of a shadowy religious leader and one-time Park mentor.
Invoking a lurid back-story of religious cults, shamanist rituals and corruption, the reports have portrayed Choi as a Rasputin-like figure whose influence over Park extended to vetting her presidential speeches and advising on key appointments and policy issues.
Yesterday morning prosecutors confiscated computers and documents from the homes of a top presidential adviser and two other aides as well as a deputy culture minister, Yonhap news agency said.
Teens in school uniforms, college students, labour activists, and middle-aged couples with young children joined the rally, carrying banners and chanting “step down Park Geun-hye”.
“I came here today to show how angry I am,” said Lee Ji-Hu, a 33-year-old housewife from Gimpo, northwest of Seoul, accompanied by her husband and two infant children in strollers.
“How can a leader have a shaman, or someone linked to a religious cult as a secret advisor and let her handle state affairs and squander taxpayers’ money like that?” Lee said.
“I feel so ashamed ... I can’t let our country where my children will live be corrupted like this,” she added.
Similar protests also took place in several provincial cities, including the country’s second largest city, Busan.
“She must step down,” Lee Jae-myung, mayor of Seongnam city south of Seoul and a vocal critic of the government, said to a loud cheer from the crowd.
“If Park Geun-hye is no longer president, will our lives be any worse off and will the tension with North Korea be any worse?” he asked the crowd, which responded “No!”
About 8,000 people attended the rally, according to police, organised by a group of left-leaning civic groups.
Organisers said that up to 30,000 people took part in the march through the capital.
“It’s become clear the people made a wrong decision and picked the wrong president,” Jeong Hong-woo, 22, told Reuters at the rally.
Police in riot gear faced some protesters as they tried to march on the presidential Blue House.
Park is in the fourth year of a five-year one-term presidency.
Opposition parties have demanded a thorough investigation, but have not raised the possibility of impeaching her.
Park’s office said late on Friday that she ordered her senior secretaries to tender their resignations, and she will reshuffle the office in the near future.
Her chief of staff separately offered to resign earlier, the office said.
The deepening crisis over Choi has sent Park’s public support to an all-time low.
In one opinion poll, more than 40% of respondents said Park should resign or be impeached.
Prosecutors are investigating two of Park’s aides who allegedly helped Choi get access to drafts of Park’s speeches and set up two foundations with about 50bn won ($44mn) in contributions from conglomerates that she later benefited from, South Korea’s Yonhap news agency reported.
The presidential office said that it was co-operating with the prosecutors’ investigation, including a request for documents.
A public apology by Park on Tuesday – for giving Choi access to draft speeches during the early months of her presidency – has done little to deflect demands that the president reveal the full extent of her ties with Choi and whether Choi gained favours from the relationship.
Choi said in a newspaper interview on Thursday from Germany, where she was staying, that she read and revised Park’s speeches early in the presidential term, but denied all allegations she interfered in state affairs.
Park is the latest South Korean leader to be embroiled in scandal involving family or friends.
As well as demanding Park stand down, civic groups and students want criminal charges brought against her aides and others who helped Choi have access to government documents.
However, the real focus of public anger has been the extent to which the president – the daughter of South Korea’s late military leader Park Chung-hee – apparently allowed herself to be controlled by a such a cult-like figure.
The head of the main opposition Minjoo Party said it was like discovering you were being ruled by a “terrifying theocracy”.
Choi is the daughter of the late Choi Tae-min, who married six times, had multiple pseudonyms and set up his own religious group known as the Church of Eternal Life.
Choi Tae-min first befriended a traumatised Park after the 1974 assassination of her mother, who he said had appeared to him in a dream, asking him to help her daughter.
Park Geun-hye subsequently formed a close bond with Choi Soon-sil that endured after Choi Tae-min’s death in 1994.
Choi Soon-sil’s ex-husband served as a top aide to Park until her presidential election victory in 2012.
Choi left the country for Germany in early September as reports of her alleged influence-peddling began to emerge.
Her lawyer has said she is well aware of the gravity of the situation and was willing to return home “to be punished if she did anything wrong”.
Prosecutors have detained two people close to Choi for questioning, including one who told reporters that Choi had been behaving as Park’s de-facto regent.