Kiir's comments, made during a trip to China, signal a rise in rhetoric between the rival nations, which spent decades at war with each other.
Neither side has officially declared war, but they have been drawing closer to a full-scale war in recent weeks over the unresolved issues of oil revenues and their disputed border. The violence has drawn alarm and condemnation from the international community, including from President Barack Obama.
South Sudan won independence from Sudan last year as part of a 2005 peace treaty that ended decades of war that killed 2 million people. Sudan President Omar al-Bashir gave a fiery speech last week in which he said there will be no negotiations with the "poisonous insects" who are challenging Sudan's claim to disputed territory near the border.
Kiir arrived in China late Monday for a five-day visit to lobby for economic and diplomatic support. China's energy needs make it deeply vested in the future of the two Sudans. Beijing is uniquely positioned to exert influence, given its deep trade ties to the resource-rich south and decades-long diplomatic ties with Sudan's government in the north.
Sudanese Antonov warplanes dropped eight bombs overnight in Panakuac, where there was ground fighting on Monday. Southern Col. Philip Aguer said. -- AP