Saudi-owned Al Arabiya TV said the two sides had agreed to indirect talks without providing details. The army and RSF did not immediately comment.
Earlier on Wednesday, Sudan army leader General Abdel Fattah al-Burhan spoke with Saudi foreign minister Faisal bin Farhan, a statement from the Sovereign Council he leads said.
Artillery and air strikes continued overnight, with residents in southern and eastern Khartoum and northern Bahri reporting sounds of artillery and gun clashes on Tuesday morning.
Looters, some of whom Khartoum residents and neighborhood committees said belong to the RSF, have pillaged neighborhoods, stealing cars, breaking open safes, and occupying homes.
The island of Tutti, which lies just north of main battlegrounds such as the presidential palace, has been besieged by the RSF, according to Emergency Lawyers, a rights group.
The RSF had blocked access to the island for eight days, cutting off food supplies and healthcare, the group said in a statement. It also said RSF members had shot at anyone who tried to leave the island, leading to the death of one man.
Overnight, the two forces clashed in the streets of the city of Omdurman, around the army's Engineers Corps base. The army, which tends to prefer air strikes to ground fighting, was able to maintain its positions around the base but could not push back the RSF, which controls most of the rest of the city.
"Our neighborhood has become a war zone. There are fierce clashes and strikes all around us because our house is next to the Engineers' Corps," said 45-year-old Jawahir Mohamed.
"We are scared of dying but we are also scared of leaving our house and being burgled," she added.
Looters, some of whom Khartoum residents and neighborhood committees said belong to the RSF, have pillaged neighborhoods, stealing cars, breaking open safes, and occupying homes.
Saudi Arabia and the United States had brokered talks that had led to imperfectly-observed cease-fires with the aim of providing humanitarian assistance. But talks collapsed last week after the mediators said there had been numerous serious violations.
Meanwhile, more than 400,000 civilians have been driven across Sudan's borders and more than 1.2 million out of Khartoum and other cities. At least 175,000 have made the journey to Egypt, where many have experienced days and weeks-long delays in border towns with few services.
On Tuesday Burhan's special envoy Ambassador Dafallah al-Haj discussed the difficulties facing Sudanese refugees with Egyptian foreign ministry officials and received assurances that border roadblocks would be relieved, a Sudan foreign ministry statement said.