Al-Dirdiri Mohamed Ahmed said the points agreed on during the talks, the second round within a week, would be announced on Wednesday morning.
While the terms of the agreement have not been released publicly, a source at Sudan’s foreign ministry told Al Jazeera that the agreement is a “political” and a “confidence-building measure agreement”.
“The agreement also made a list of priorities and procedures the parties have agreed upon for future discussions,” he added.
It is still not clear, however, if the agreement would include a ceasefire deal between the warring parties at this point.
Steps to end the ongoing fighting, securing oil field areas, and troops redeployment are believed to be on the agenda of the meeting.
“I came to this meeting with an open mind and hope my brother, Riek, did the same,” Kiir said at the beginning of the talks, which were mediated by Sudan’s President Omar al-Bashir and also attended by Ugandan President Yoweri Museveni.
I came to this meeting with an open mind and hope my brother Riek did the same
For his part, Machar told reporters: “We came to Khartoum to look for peace”, although he said his own invitation had come “late”, without elaborating.
“There is a chance for peace and there is a way to achieve peace,” said Machar.
Kiir and Machar met face-to-face for the first time in several years in Addis Ababa last week under pressure to end the country’s bloody civil war.
The fledgeling nation, which was carved out of Sudan in 2011, descended into civil war in 2013 following a political conflict between Kiir and his then Vice President Machar, who was accused of plotting a coup.
A power-sharing agreement signed between the two parties in August 2015 did not end the fighting. Machar has been in exile since he left Juba in July 2016 following clashes between his supporters and government forces.
In May, the UN Security Council voted to renew sanctions for 45 more days against six South Sudanese officials that include travel ban and assets freeze for “blocking peace in South Sudan”.
More than four years of civil war has since killed tens of thousands of people and forced about four million South Sudanese to flee their homes. Multiple ceasefires and peace efforts have so far failed to end the deadly violence.
Meanwhile, Sudan and South Sudan signed on Tuesday an agreement under which more southerly nation would resume pumping of its oil through Sudanese territory.
The agreement was signed by Sudan’s Minister of Petroleum and Gas Azhari Abdul-Qadir and Southern Sudan’s Energy Minister Ezekiel Lol.
Under the deal, Sudan will rehabilitate oilfields in South Sudan that ceased operating for five years because of the civil war.
The Sudanese minister of petroleum said that the work will begin officially on July 2.
For his part, the South Sudan energy minister said that the agreement is a step in the right way to strengthen oil cooperation in support of the peace process.