The two sides, who have been fighting since April, have previously agreed to and then promptly violated ceasefires and commitments to facilitating aid and protecting civilians.
The deal announced by SPA does not include a ceasefire and so is not expected to lessen the fighting.
Fighting in Sudan's Darfur region and the capital Khartoum has picked up since the two sides reconvened for talks, brokered by Saudi Arabia, the United States and regional African bloc IGAD, last month, incurring heavy civilian casualties.
The two sides on Tuesday blamed each other for a massive fire at the al-Jaili oil refinery on the outskirts of Khartoum.
Refugees and eyewitnesses arriving in Chad have also accused the RSF of reviving bloody ethnic violence in the West Darfur town of El Geneina.
The RSF has described the fighting there as tribal violence.
Mediators expressed regret that the two parties had not yet reached an agreement for a ceasefire, the statement released by SPA said.
They urged the warring parties "to put the interests of the Sudanese people first, put down their weapons, and engage in negotiations to end this conflict".
Instead, the two sides agreed to work with the United Nations humanitarian agency OCHA to resolve impediments to humanitarian aid access, the statement said, as well as to set up a line of communication between the army and RSF and tone down inflammatory rhetoric.
They also agreed to apprehend prison escapees. Soon after the war began, members of ex-president Omar al-Bashir's Islamist regime said they were part of a wider break-out of prisoners.
The war erupted on April 15 after weeks of rising tension between the two sides over a plan to integrate forces as part of a transition from military rule to civilian democracy.
