There was no immediate response from Machar or his party to the allegations.
Machar's party has previously denied government accusations that it backs the White Army, an ethnic militia largely comprising Nuer youths, which clashed with the army in the northeastern town of Nasir this month, triggering the latest crisis.
In response to the fighting, Kiir's forces rounded up several of Machar's senior allies, including the petroleum minister and the deputy head of the army.
There have been clashes in recent days between forces loyal to the two men outside Juba and elsewhere.
UN secretary-general Antonio Guterres said on Friday the peace process was in a shambles and asked its leaders to lay down their weapons and put the people of South Sudan first.
“Let's not mince words: what we are seeing is darkly reminiscent of the 2013 and 2016 civil wars, which killed 400,000 people,” Guterres told reporters in New York, referring to episodes in the conflict.
Kenyan President William Ruto, who chairs the East African Community bloc, said he had spoken to Kiir about Machar's detention.