The East African regional bloc, the Intergovernmental Authority on Development, IGAD, had invited the foes — Sudan's army chief Abdel Fattah al-Burhan and Mohamed Hamdan Dagalo, commander of the paramilitary Rapid Support Forces — to a meeting in Ethiopia's capital, on Monday.
Neither attended the talks in Addis Ababa, although the RSF sent a representative to the "quartet" meeting led by Kenya, South Sudan, Djibouti and Ethiopia.
Sudan's foreign ministry said on Monday that its delegation would not participate until its request to remove Kenya as chair of the talks was met.
The ministry had asked for "Kenyan President William Ruto (to) be replaced... in particular because of his partiality," a statement said.
Sudan had earlier alleged that Nairobi "adopted the positions of the RSF militia, sheltered its people and offered them various forms of support."
In a communique released after Monday's meeting, the quartet acknowledged the absence of a delegation from the Sudan Armed Forces, SAF, "in spite of the invitation and confirmation of attendance."
The statement did not make mention of the request by the SAF on the removal of Kenya as chair but emphasized "the centrality of IGAD in coordinating the different diplomatic tracks alongside the African Union" in an effort to coordinate a framework to deliver a lasting peace deal.
The quartet noted the escalating conflict, repeated violations of various cease-fire agreements and the spread of violence outside of Khartoum other parts of Sudan "where (the conflict) is assuming ethnic and religious dimensions thereby threatening to deepen the polarization in the country."
The group said it would request that the African Union look into possibly deploying in Sudan the East Africa Standby Force — usually tasked with election observer missions —"for the protection of civilians and ... humanitarian access."
Meanwhile, the Sudanese civil aviation authority extended the closure of the country's airspace until July 31, with the exception of humanitarian aid and evacuation flights with permission from authorities, Khartoum International Airport said on Monday.
Sudanese airspace has been closed to regular traffic since the conflict erupted in mid-April.
Around 3,000 people have been killed in the conflict, while nearly three million have been forced to flee their homes.
Information in this report came from Agence France-Presse and Reuters.