South Korean President Yoon Suk Yeol walked out of a detention centre in Seoul on Saturday after prosecutors decided not to appeal a court decision to cancel the impeached leader's arrest warrant on insurrection charges.

Yoon remains suspended from his duties, and his criminal and impeachment trials continue over his short-lived martial law imposition on December 3.

The Seoul Central District Court cancelled Yoon's arrest warrant on Friday, citing the timing of his indictment and "questions about the legality" of the investigation process.

"First of all, I would like to thank the Central District Court for their courage and determination in correcting the illegality," Yoon said in a statement.

His lawyers said the court decision "confirmed that the president's detainment was problematic in both procedural and substantive aspects," calling the ruling the "beginning of a journey to restore rule of law".

Prosecutors could not immediately be reached for comment.

In Yoon impeachment trial, the Constitutional Court is expected to decide in coming days whether to reinstate him or remove him from office.

Yoon, the first South Korean president to be arrested while in office, has been in custody since January 15.

On Saturday, Some 38,000 Yoon supporters rallied in Seoul, while 1,500 people demonstrated against him, Yonhap news agency reported, citing unofficial police estimates.