After a decades-long fight for independence, South Sudan peacefully broke away from Sudan in 2011.
Relations between the two countries have been strained since the split and both countries have suffered from instability and sporadic violence. Kiir's government in South Sudan recently faced a challenge from forces loyal to former Vice President Riek Machar.
Violence began as a political dispute but has since taken on ethnic dimensions, with tribes attacking each other. The central government in each country blames the other for harboring rebels hostile to them.
The outbreak of fighting is costing Sudan lost oil revenue.
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Al-Bashir said the Saturday visit "has served its purpose" and expressed hope that the coming days would witness full normalization of relations and reopening of common borders between the two countries. He said he and Kiir discussed "cooperation between the two countries for achieving peace and security," according to the state news agency.
The two sides last year signed a number of deals that addressed issues of border trade, security arrangements and oil sharing accords.
They also agreed to avoid hosting any rebel elements fighting the other side. Kiir said he would come back to Khartoum soon for further meetings with other Sudanese officials.