South Sudan, which won independence from Sudan in 2011, has been playing a mediation role through the regional bloc IGAD to try to resolve the conflict between the paramilitary RSF and army chief Abdel Fattah Al Burhan's forces.
Sudan's foreign ministry said in a statement published on Thursday that it had issued an "official protest memorandum" to Juba to express its "strong denunciation" over a visit this week by one of RSF leader General Mohamed Hamdan Daglo's advisers.
Gen Daglo's envoy Yusif Isha held talks with South Sudanese President Salva Kiir and IGAD officials in Juba on Wednesday and later told a press conference the RSF was "ready to take part in any step taken by him (Kiir) to reach a lasting peace in Sudan."
Mr Kiir has held several conversations with Sudan's de facto leader Gen Burhan and his deputy-turned-rival Gen Daglo, and also hosted a Burhan envoy in Juba on May 8.
South Sudan's government "has continued to play its part within IGAD with absolute impartiality," the foreign ministry said in a statement on Friday.
"The notion of mediation entails the engagement of all parties with equal measure," it added.
Since the conflict erupted in Khartoum in mid-April, around 1,000 people have been killed and fighting is raging despite several ceasefire deals.
The United Nations has warned it expects more than one million people to flee to neighbouring countries this year, and Juba said Friday that over 60,000 have so far crossed into South Sudan.
The comments came as Sudan's capital Khartoum and sister city Bahri came under renewed air attack on Friday.
Mass looting by armed men and civilians alike is making life an even greater misery for Khartoum residents pinned down by fierce fighting between the regular military and paramilitary Rapid Support Forces (RSF), witnesses said.
At an Arab League meeting there on Friday, a statement by Sudan's envoy accused the RSF of looting and rape, and of violating a succession of ceasefires.
"We trust that you will stand by the Sudanese army and will accompany us in the next step of reconstruction," envoy Dafallah al-Hajj added.
The RSF has accused the army of starting the conflict and violating ceasefires. It says that those who have committed crimes are wearing stolen RSF uniforms.
Air strikes on Friday targeted districts in eastern Khartoum and witnesses reported hearing anti-aircraft weapons used by the RSF. Bahri and Sharg el-Nil across the Nile river from Khartoum were subjected to air strikes overnight and Friday morning.
"On the road I saw about 30 military lorries destroyed by [air] strikes. There were bodies everywhere, some of them army and some RSF. Some had started decomposing. It was really horrible," said Ahmed, a young man making his way through Bahri.
The RSF is embedded in residential districts of much of Khartoum and adjoining Bahri and Omdurman, drawing almost continual air strikes by the regular armed forces.
Witnesses said the army had also started placing barriers on some roads in southern Khartoum to keep the RSF away from an important military base there.
Fighting also flared in the city of Nyala, capital of the South Darfur region in the south-west, for a second day after weeks of relative calm.
Heavy gunfire and artillery detonations went on all day in Nyala. A local market caught fire and it was difficult for those injured to get to hospitals, local activists said. The Darfur Bar Association, a human rights group, said that 27 people had been killed and dozens injured so far.
They called on the RSF, whose movements it blamed for the flare-up, to recommit to a locally brokered truce.
Militia attacks and subsequent clashes in the West Darfur city of Geneina have claimed the lives of hundreds.