Week-long talks between Sudan and South Sudan broke up Thursday with little progress on the establishment of a secure border zone.
"We will go back for consultation with our respective headquarters and come back within one week," said Omer Dahab, a member of Khartoum's delegation.
When asked whether the two sides had agreed on a demilitarized buffer zone along the disputed border, Dahab said "unfortunately not."
Both sides were in the Ethiopian capital for the latest round of African Union-led peace talks following weeks of fighting in April that brought the two foes back to the brink of all-out war.
Following the deadly violence, the United Nations and the African Union passed resolutions urging the two countries to solve border, security and oil disputes before an August 2 deadline.
A new round of talks is due to start in Addis Ababa on July 5.
The South's chief negotiator Pagan Amum said the two sides failed to reach an agreement on the secure border because Khartoum rejected an AU map that places a disputed area in South Sudan's territory.
"There has been no agreement on the process on how to settle these disputes on claims to disputed territories along the border," Amum told reporters.
"We are left with one month and the two countries have not resumed negotiations on all the outstanding issues," he added.
However, Sudan's Defense Minister Abdelrahim Mohamed Hussein said he was satisfied with the progress of the talks so far.
"The most important thing... is the reduction of the tension and this is what we are doing now," he told reporters. "We are confident that we will achieve the results."
The AU's chief mediator, Thabo Mbeki, called on the international community to support the ongoing talks and praised both Sudan and South Sudan for their "serious" approach in the just concluded round of negotiations.
"The parties have demonstrated great maturity and seriousness in their approach to the negotiations... this can only be good for the citizens of Sudan and South Sudan," he said in a statement.
Talks between Sudan and South Sudan kicked off after the South gained independence from Khartoum last July.
The South took with it 75 percent of the region's oil resources, but the processing and exporting facilities remain in the North.
In January, Juba cut off oil exports to the North, losing 98 percent of its revenues, and crippling both economies.
Khartoum and Juba have since introduced austerity measures in the wake of the financial crisis.