Investigators probing Yoon over his December 3 martial law on Friday again failed to serve an arrest warrant, blocked by presidential security service guards who formed a human chain to prevent access to Yoon.
The arrest warrant, the first for a sitting president, expires at midnight on Monday.
The Corruption Investigation Office for High-ranking Officials (CIO) said on Monday they had requested an extension of the warrant in court, but declined to say how long the extension would last.
Yoon, who has been impeached over his martial law declaration, is under criminal investigation for possible insurrection.
The US had expressed "serious concerns" over President Yoon Suk-yeol's actions, Antony Blinken said. (AP PHOTO)
The brief six-hour martial law declaration plunged one of Asia's strongest democracies into uncharted territory with the impeachment of not only Yoon, but also the prime minister who become acting president, and the appointment of a second acting leader.
Yoon's actions drew a rare rebuke from officials in Washington including Blinken's deputy, Kurt Campbell, who has said it was "badly misjudged".
Speaking on Monday after his meeting with South Korean Foreign Minister Cho Tae-yul, Blinken said Washington had expressed "serious concerns" to Seoul over some of the actions Yoon took during the course of his martial law declaration.
But the events unfolding since then had been a reflection of South Korea's brand as a democratic success, "which is remarkably strong", Blinken said at a news conference.
"The response that we've seen, and that we expect to continue to see, is one that is peaceful and fully consistent and in accordance with the constitution and the rule of law."
Yoon was impeached by parliament on December 14 and suspended from presidential duties.
South Korean President Yoon Suk-yeol was impeached over his short-lived declaration of martial law. (AP PHOTO)
The Constitutional Court is trying the case to decide whether to remove him from office permanently or reinstate him.
The CIO, which is leading the criminal insurrection probe into Yoon, has sent a notice to police requesting them to take over execution of the arrest warrant.
A police official said at a news briefing that police believed there was a legal dispute over such a transfer and would discuss it with the CIO.
Yonhap news cited a police official as saying the arrest warrant will now be executed under the authority of the police joint investigation team and the CIO.
Yoon's lawyers have argued the CIO anti-graft force has no authority under South Korean law to investigate any case involving insurrection accusations.
President Yoon Suk-yeol's supporters have vowed to keep rallying until they "reap the results". (AP PHOTO)
The unprecedented attempt to arrest an incumbent president has intensified duelling rallies by those supporting Yoon, with the "Stop the Steal" slogans popularised by US President-elect Donald Trump voters, and those calling for Yoon's punishment.
On Monday, a group of hardcore Yoon supporters led by Christian pastor Jun Kwang-hoon held a news conference and described the fight for Yoon as an "international battle" for freedom.
Jun said Yoon supporters would continue rallies outside his residence until they "reap the results".
