Mr Kiir's government said its forces were in control of all cities, but he has offered to talk to Mr Machar.
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Mr Kiir said a group of soldiers supporting Mr Machar had tried to take power by force on Sunday night but were defeated.
He said the clashes began when uniformed personnel opened fire at a meeting of the governing party, the Sudan People's Liberation Movement (SPLM).
But Mr Machar told the BBC World Service's Newsday programme on Wednesday: "There was no attempted coup."