"My apologies to the public," she said. "Please forgive me."

Her lawyer, Lee Kyung-jae, has indicated that she will cooperate fully with the investigation.

Lee told reporters Sunday "she is deeply remorseful that she had caused frustration and despondency among the public."

The prosecutor's office has promised a quick and thorough investigation, according to YTN.

Significant influence

Choi's family has long held influence over Park, David Kang, Director, Korean Studies Institute at the University of Southern California, tells CNN.

"The friend's father, Mr Choi, was head of a cult-like religion back in the 70s and began to mentor Ms. Park when she was in her early 20s," he said. "So the family has had an extraordinary influence over Park Geun-hye for essentially her entire adult life.

"It's much more than simply, 'oh she knows this person,' it's deeply intertwined, almost like they're Rasputin and Park Geun-hye is just a puppet."

Protests

"The Choi Soon-Sil crisis revealed that President Park Geun-Hye has neither the ability nor capacity to administer the government," protest leader Han Sun-bum said Saturday.

"So we've gathered to demand Park resign, and we are going to keep protesting to urge for resignation until Park steps down."

Police estimated that around 12,000 demonstrators attended the evening protest, according to the country's semi-official Yonhap news agency.

Resignations ordered

Senior secretaries are essentially aides who coordinate policy between the presidency and government ministries.

Those ordered to resign include the senior secretaries to the president for policy coordination, political affairs, civil affairs, foreign affairs and national security, public relations, economic affairs, future strategy, education and culture, employment and welfare and personnel affairs, according to the presidential office's website.

Park is expected to name new secretaries some time this week, according to local media.

But, Kang says, the problem doesn't appear to be solvable with a quick cabinet reshuffle.

"Can she rule, even if she gets rid of the cabinet? The cabinet wasn't the problem, she was the problem," he said.

Presidential apology

Park on Tuesday admitted to sharing state documents with Choi Soon-sil, who offered "her personal opinion" on Park's speeches before the presidential election in 2012.

Choi does not hold any public office.

In a televised presidential apology, Park said Choi looked at "some documents" for a certain period of time after Park took office, but didn't specify what they were.

"I am shocked and my heart is breaking for causing public concern," Park said in the live telecast. "I've done so (shared the documents) out of pure heart so that I could carefully review (the documents)."

Abandoned computer

CNN South Korean affiliate JTBC broke the news of the scandal earlier this week after revealing that it had found an abandoned computer of Choi's containing evidence she received secret documents and intervened in state affairs.

Local media and opposition parties accused Choi of abusing her relationship with Park to force big local conglomerates to donate millions of dollars to two foundations they claim she had set up.

The South Korean prosecutor's office on Thursday established a "special investigation unit" to probe the cases.

Political fallout

The incident has hit Park's approval ratings. Her weekly approval rate plunged to a record low of 21.1% Thursday, according to a local pollster Real Meter.

Park, whose presidency ends in early 2018, had approval ratings between 30% to 50% during her first three years in office. This year, however, has been a bad one for the president.

A combination of a weak economy, inadequate public communications and poor administration of state affairs, according to multiple poll results, have resulted in slipping approval scores.

Park, South Korea's first female president, is the daughter of Park Chung-hee, South Korea's leader from 1961 to 1979, who was assassinated by his own intelligence chief. The late Park is hailed by some as the mastermind behind the country's current prosperity but criticized by others as a dictator who violated human rights by crushing dissenters.