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"All of this happening is my fault. It happened because of my neglect," she said in a televised address Friday.
For the second time in two weeks Park apologized for the scandal and maintained she wasn't being controlled by anyone else.
"There are even talks of me being immersed in a cult or resorting to shamanism in the Blue House. I would like to say that this is absolutely not true," she said.
On Wednesday prosecutors issued an arrest warrant for Park's close friend and informal advisor, Choi Soon-sil, on charges of abuse of power and attempted fraud.
"I have already instructed Blue House secretary's office and security office to co-operate fully with the prosecutor's investigation. If it is necessary, I, too, am ready to co-operate to the prosecutor's investigation," Park said on Thursday.
Choi accused of abusing Park relationship
Park is accused of allowing Choi to view confidential documents and presidential speeches despite not holding an official post.
Local media and opposition parties have accused Choi of using her relationship with Park to accumulate millions of dollars in donations to her foundations.
Choi succeeded her father as leader of the Eternal Life Church after his death in 1994, and has been described as South Korea's "Rasputin."
"The family has had an extraordinary influence over Park Geun-hye for essentially her entire adult life," David Kang, a Korea expert at the University of Southern California, told CNN last week.
South Koreans take to the streets
According to Yonhap new agency as many as 12,000 demonstrators called for her resignation, saying she was unfit to run the country.
On Thursday, a new Gallup poll in South Korea found Park's approval rating was just 5%, with 89% having a negative opinion of her performance.
Among people aged less than 40, her approval was 1%. It was above 30%, overall, before the scandal.