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 agency 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 that the CIO anti-graft force has no authority under South Korean law to investigate any case involving insurrection.
On Monday, Seok Dong-hyeon, a lawyer advising Yoon, said the bid to transfer the execution of the arrest warrant is effectively an admission by the CIO that its probe and the warrant were “illegal”.
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.
“Sadly, there’s no Fox News in Korea,” it said in a statement, referring to the American cable news channel popular with Trump supporters.
Jun said Yoon supporters would continue rallies outside his residence until they “reap the results”.