In a highly personal televised address to the nation, Park said the scandal involving her long-time confidante Choi Soon-Sil was "all my fault", but denied reports linking her and Choi to a religious cult.
The scandal has shattered public trust in Park's presidency, and a new Gallup poll showed her approval rating had plummeted to just five percent -- an all-time low for a sitting South Korean president.
A formal investigation is focused on allegations that Choi, 60, leveraged her close relationship with Park to coerce local firms into donating large sums to dubious non-profit foundations that she then used for personal gain.
Park said she would not seek to hide behind presidential privilege if required to give testimony.
"If necessary, I am willing to sincerely respond to prosecutors' investigations," she said.
South Korea's constitution does not allow a sitting president to be prosecuted, but some senior officials have suggested questioning as part of a wider investigation is permissible.
Park, who appeared close to tears at times, said she had been living a "lonely life" as president and had turned to Choi for company and help.
"Looking back, I allowed my guard to drop as she stood by my side during difficult times," she said.
"I trusted my personal relationship, but was careless and not tough enough with my acquaintances," she added.
"There have been claims that I fell for a religious cult or had (shamanist rituals) performed in the Blue House, but I would like to clarify that those are absolutely not true," Park said in her address today.
In an effort to restore trust in her administration, Park has reshuffled ministers and senior advisers, bringing in figures from outside her ruling conservative Saenuri Party.
Reacting to her address, the main opposition Democratic Party insisted her changes had been cosmetic and warned that it would begin a campaign for her ouster unless further steps were taken.
Park is unlikely to step down, with analysts suggesting she will limp on to the end of her term with her power severely undermined at a time of slowing economic growth, rising unemployment and elevated military tensions with North Korea.
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