South Korean President Park Geun Hye has apologised again and said she is willing to be investigated over an influence peddling scandal involving a friend, even as she described herself as a lonely head of state so reliant on this friend that she had let her guard down.

In a nationally televised address yesterday morning, Ms Park acknowledged that "it's all my fault" and said she would take responsibility for the damaging scandal that has sparked public anger and led to calls for her to step down.

The latest Gallup poll shows that her approval rating has plunged to a mere 5 per cent, down from 10 per cent earlier this week.

With tears brimming in her eyes and her voice trembling, Ms Park said her "heart is breaking" and that "I cannot forgive myself".

"I am fully prepared to take responsibility for any wrongdoing on my part," she said, adding that she will do her best to cooperate with the prosecution.

Pressure has been mounting on Ms Park to subject herself to investigations as public resentment grows over how she allegedly allowed her friend Choi Soon Sil to abuse their friendship to meddle in state affairs for Ms Choi's own gain.

The prosecutors have widened their probe, arresting Ms Choi for fraud and abuse of authority among other charges, and detaining two former presidential aides Ahn Jong Beom and Jeong Ho Seong for alleged links to Ms Choi.

If Ms Park does face questioning, she will be the first sitting president in South Korean history to be investigated by prosecutors.

Analysts said the probe can happen as early as next week.

Ms Park, meanwhile, has nominated university professor Kim Byong Joon as the new prime minister to take charge of domestic affairs as people feel she has lost legitimacy to run the country.

Seoul National University's law professor Lee Jae Min said the probe will most likely be conducted in writing, with prosecutors giving the President a list of questions to answer. The testimony collected can then be used in the ongoing case.

"It is unimaginable for a sitting president to appear in the prosecutor's office to face questioning directly. If she does, it will mean her presidency is virtually over," he said.

Ms Park's national address came 10 days after she first apologised on Oct 25 for allowing Ms Choi to edit some of her speeches. Their friendship goes back over 40 years and Ms Choi is the daughter of a religious cult figure who had served as mentor to both Ms Park and her father, the late president Park Chung Hee.

Yesterday, Ms Park admitted that she was blinded by her trust in Ms Choi who "stayed by my side through the most difficult times of my life". But she denied rumours that she was addicted to a cult and conducted shamanistic rituals in the presidential Blue House.

Senior research fellow Lee Myon Woo of the think-tank Sejong Institute said Ms Park's apology was a "good move", but noted that her harshest critics will not be satisfied regardless of what she says.

The main opposition Democratic Party's leader Choo Mi Ae has said Ms Park's apology lacked sincerity and urged her to "remove herself from state affairs".

Calls for the President to resign are still raging with organisers of a daily protest expecting tens of thousands of people to take to the streets today to do the same.

Businessman Justin Jang, 37, said: "She has lost her credibility completely. We have to wait and see if she will indeed be investigated. We cannot simply trust what she says."