South Korea's arrested President Yoon Suk Yeol does not intend to take part in a second day of questioning on Thursday, his lawyer said, further stonewalling a criminal probe into whether he committed insurrection with his martial law bid.

Yoon, the first sitting South Korean president to be arrested, was taken to the Seoul Detention Centre on Wednesday evening after refusing to cooperate, where he was expected to have spent the night in a solitary cell.

Authorities have 48 hours to question the suspended president, after which they must release him or seek a warrant to detain him for up to 20 days.

Yoon's refusal to cooperate with investigators comes as the Constitutional Court is due to hold a second hearing in his impeachment trial to determine whether to remove him permanently or reinstate his presidential powers.

South Korea is grappling with a political crisis sparked by Yoon's brief attempt to impose martial law on December 3 that was voted down by parliament.

Yoon's arrest on Wednesday ended a weeks-long standoff with authorities after police swooped before dawn on his fortified hillside villa in Seoul to the despair of followers at the site.

Yoon said he turned himself in for questioning by corruption investigation officials to prevent what he called the risk of "unsavoury bloodshed", though he continued to protest that it was an illegal investigation and invalid arrest warrant.

Yoon has up to now refused to talk with investigators who had prepared a questionnaire of more than 200 pages, an official from the Corruption Investigation Office for High-ranking Officials (CIO) that is heading the criminal inquiry said on Wednesday.

The embattled leader did not even reply to a question, a CIO official said.

His questioning is due to resume at 2 pm local time, on Thursday, according to CIO.

But Yoon Kab-keun, one of Yoon’s lawyers, said in a text message to reporters that Yoon would not show up for the questioning.

Yonhap reported the same lawyer as citing Yoon's health as a factor and saying further questioning was pointless, without elaborating.

The CIO official said he understood it was possible to forcibly bring Yoon for questioning but would make further checks on relevant laws.

A small crowd of protesters supporting Yoon gathered and sat on a road outside the CIO office, calling the president's arrest illegitimate.

Opinion polls show a majority of South Koreans support impeaching Yoon, but the attempts to arrest him appear to have rallied his hardcore supporters. (Reuters)