"The people of South Sudan should remain calm and patient as we work with the African Union to resolve this impasse with Sudan," Kiir told reporters, while condemning the "aggressive attitude" of Khartoum.
Sudan on Sunday put on hold nine security and economic pacts with South Sudan, including on vital oil shipments, but said Khartoum remained committed to good relations if Juba ended support for rebels.
The move followed an order on Saturday from President Omar al-Bashir to shut the pipeline carrying South Sudanese crude for export.
"This latest turn of events brings into question the credibility" of the African Union mediators, Kiir said, but added "we remain optimistic that they will intervene accordingly."
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"We urge both regional and international governments to diplomatically engage with Sudan in order to protect the lives of the citizens of both nations, and to encourage Sudan to engage in peaceful dialogue with their internal rebellion," Kiir said.
"While President al-Bashir has declared jihad and is mobilising for war, I maintain my pledge to you and the world that I will not take the people of South Sudan unnecessarily back to a state of war," he added.
South Sudan became independent two years ago under a peace deal that ended a 22-year civil war. It separated with most of Sudan's oil production but the export infrastructure remained under northern control.
The two sides had not been able to agree on how much Juba would pay to use the pipeline.
Both impoverished nations stand to earn billions of dollars if the oil flows.
Sudanese SPLM-N rebels, who fought alongside the civil war rebel movement which now rules South Sudan, have been battling Khartoum for two years in South Kordofan and Blue Nile states.