Riek Machar’s statement, obtained by The Associated Press, accuses the government of pushing ethnic groups into fighting.
Machar is Nuer. The civil war that erupted in December 2013 between supporters of Kiir and Machar has long shown ethnic tensions.
South Sudan government spokesmen did not immediately comment.
Machar on Saturday made his first political statement since fleeing South Sudan in August after fighting erupted in the capital, Juba, in July. The statement called for armed resistance to the government in which Machar had served as vice president this year under a fragile peace deal.
Machar is now in Sudan. A colleague said Machar is not allowed to speak publicly according to the terms of his stay there. The colleague spoke on condition of anonymity because they were not authorized to speak to the media.
Also on Monday, Sudan distanced itself from Machar.
The SUNA news agency quoted Foreign Minister Ibrahim Ghandour as saying Sudan will not serve as a launching pad for any armed opposition activities against South Sudan.
Ghandour apparently was referring to a recent meeting in Khartoum of Machar’s opposition party. Following that meeting, Machar’s camp issued the statement calling for armed resistance.
The foreign minister also said Sudan is interested in peace in South Sudan, where the civil war has killed tens of thousands and sent more than one million refugees fleeing the country.
South Sudan, the world’s youngest country, won its independence from Sudan in 2011 after decades of fighting.