The latest round of Jeddah talks aim to bring a pause, if not complete end, to fighting that broke out in April as the army and paramilitary Rapid Support Forces (RSF) vied for power.
More than 3.5 million people have been uprooted due to the fighting, which has caused one of the world's worst humanitarian situations.
The army's delegation left Jeddah after differences on issues "including the rebels evacuating civilian homes in the capital and public facilities, hospitals and roads" led to a lack of agreement on a ceasefire, the army said.
In a response, the RSF said that a joint committee had observed that the RSF had vacated all the sites it had visited in the capital.
The RSF also disputed the army's statement that the talks had been "indirect," saying the two delegations had sat down in person, and that its delegation remained in Jeddah.
It blamed the breakdown in talks on what it said was the army's demand to end a blockade on its headquarters in central Khartoum.
While the two warring sides have shown openness towards mediation efforts led by regional and international actors, none has resulted in a sustained ceasefire.
The two sides resumed talks, facilitated by Saudi Arabia and the United States, in Jeddah this month.
(Reporting by Khalid Abdelaziz; Writing by Ahmed Elimam; Editing by Andrew Heavens, Nick Macfie and Sandra Maler)
