"We've agreed to hold a security committee meeting in January," Karti said at a joint press conference with Benjamin in Sudanese capital Khartoum.
He said he had hopes that the meeting would be held during the first half of the month.
Karti said Sudan and South Sudan had sought to resolve their differences through negotiation and away from the media.
Benjamin, for his part, denied accusations that his country had supported Sudanese rebels. He said both Sudan and South Sudan had mechanisms for resolving these security doubts.
"There are doubts on both sides," Banjamin said. "We are able to overcome them," he added, ruling out the possibility of war between Sudan and South Sudan.
On December 21, South Sudan's Foreign Ministry summoned the Sudanese ambassador in Juba to protest statements by a Sudanese army general who threatened to pursue Sudanese rebels into South Sudanese territory.
"The ambassador was informed that such statements do not benefit bilateral relations," South Sudanese Foreign Ministry spokesman Mawien Makol told The Anadolu Agency at the time.
He said Benjamin would soon visit Khartoum for talks with his Sudanese counterpart.
Earlier in December, Sudan's intelligence chief, Mohamed Atta, threatened to pursue rebel groups opposed to Khartoum inside South Sudan, accusing Juba of funding the rebel forces.
South Sudan has repeatedly denied accusations to this effect in the past.
South Sudan seceded from Sudan in 2011 in line with a 2005 peace treaty that ended Africa's longest civil war.
Since 2011, a number of rebel groups have waged an active insurgency against Khartoum, particularly in the southern and western parts of Sudan.