By Hyunsu Yim and Jack Kim

SEOUL (Reuters) - South Korea's impeached President Yoon Suk Yeol refused on Monday to be questioned by investigators under a probe into whether he committed insurrection, as dozens of his supporters faced arrest over a violent rampage on a court building.

Authorities said security was being beefed up at the Seoul Detention Centre where Yoon is being held as a pre-trial inmate and at the Constitutional Court which is holding an impeachment trial to decide whether to permanently remove him from office.

Yoon became the first incumbent South Korean president to be arrested last week over his short-lived declaration of martial law on Dec. 3.

On Sunday, he was formally processed for detention, including having his mugshot taken, after a court approved a warrant, citing concern the suspect could destroy evidence.

Following the midnight ruling, angry Yoon supporters stormed the Seoul Western District Court building early on Sunday destroying property and clashing with police who were at times overpowered by a mob wielding broken barricades to attack them.

Police are planning to arrest 66 people for trespass, obstruction of official duty and assaulting police officers, Yonhap News Agency reported.

Other offenders were still being identified and police will also take legal action against them, acting Justice Minister Kim Seok-woo told a parliament judiciary committee.

Acting President Choi Sang-mok expressed deep regret over the "illegal violence" at the court building and also urged police to enforce the law strictly to prevent a repeat of what happened on Sunday.

LIVESTREAMED INTRUSION

Hundreds of protesters, some blasting fire extinguishers at lines of police, broke through a cordon to enter the court building soon after the 3 a.m. ruling on Sunday to approve the detention of Yoon.

Some of them were seen in video footage roaming halls where the offices of judges were located calling out the name of the judge who approved the warrant.

At least one judge's chamber was broken into by force, Chun Dae-yup, the head of the National Court Administration, said.

Several of those involved livestreamed the intrusion on YouTube, with footage showing protesters trashing the court and chanting Yoon's name. Some streamers were caught by police during their broadcasts.

Yoon's refusal to appear for questioning on Monday at the Corruption Investigation Office for High-ranking Officials (CIO), which is leading the criminal probe, comes after he has repeatedly refused to cooperate with the investigation.

His lawyers have argued that his arrest on Wednesday and the warrant issued for his detention are illegal because they were backed by a court that is in the wrong jurisdiction and the CIO itself has no legal authority to conduct the probe.

Insurrection, the crime that Yoon may be charged with, is one of the few that a South Korean president does not have immunity from and is technically punishable by death. South Korea, however, has not executed anyone in nearly 30 years.

Yoon said through his lawyers that he found Sunday's rampage at the court "shocking and unfortunate", calling on people to express their opinions peacefully.In the statement, Yoon also said he understood many were feeling "rage and unfairness", asking police to take a tolerant position.

(Reporting by Hyunsu Yim and Jack Kim; Editing by Ed Davies and Saad Sayeed)