According to Cheong Wa Dae spokesman Kim Eui-kyeom, Mr Moon gave the orders in connection with cases involving late actress Jang Ja-yeon, former vice justice minister Kim Hak-eui, and the ongoing investigation surrounding the nightclub Burning Sun.

"The common factor is that (the cases concern) developments that took place among the privileged, and there is circumstantial evidence suggesting that the prosecutors and police purposely conducted incomplete investigations, and actively prevented the truth from being revealed," Mr Moon was quoted as saying.

Mr Moon was also quoted as saying that unless the truth about these cases is revealed, the police and prosecution cannot regain their credibility and that Korea will remain an unjust society.

"The cases are of the past, but revealing the truth and being reborn as investigative organisations that are trusted by the people is something the leadership of the prosecution and the police must ensure. The future of the organisations is on the line."

Read also: Police accelerate probe into Burning Sun scandal

Ms Jang took her own life on March 9, 2009, at the age of 29. At the time, it was revealed that the actress left several pages of handwritten notes detailing sexual and physical abuse by powerful figures.

The notes also included a list of people she said she was coerced to have sex with, including members of the founding family of the Chosun Ilbo newspaper. The list of names was not publicly revealed and no powerful figure has been charged.

Ms Jang's former colleague Yoon Ji-oh, 31, spoke to the police last week as part of a reopened probe into the suicide. She is now living in a safe house and getting personal police protection.

Mr Kim Hak-eui is a former vice justice minister who was accused in 2013 of accepting bribes in the form of sexual services, allegedly against the will of the woman involved, in a case involving a contractor named Yoon Jung-cheon.

Despite video clips that appeared to show Mr Kim engaged in sex acts, the prosecution threw the case out citing lack of evidence. When a woman claiming to be the woman in the video came forward in 2014, alleging that Mr Kim had raped her multiple times while she was drugged, the prosecution again threw the case out, citing lack of evidence and calling the woman's testimony unreliable.

But National Police Agency Commissioner General Min Gap-ryong recently testified at the National Assembly that Mr Kim was easily identifiable in at least some of the videos.

Both cases are being reviewed by a fact-finding commission within the Supreme Prosecutors' Office. The commission's mandate is set to expire at the end of the month, but there have been growing calls for an extension.

The ongoing Burning Sun case, which began as an assault case in which the alleged victim accused the police of collusion with club management, continues to expand.

The investigation has placed Seungri, a member of the boy band Big Bang, under suspicion of a number of illegal activities including arranging sexual services for potential investigators. In addition, singer Jung Joon-young has been accused of illegally filming himself having sex with women and sharing the videos with other entertainers.