The clashes have particularly intensified in the capital Khartoum, and Gezira and Sinnar States in central Sudan.
According to sources and eyewitnesses, the SAF is continuing its offensive launched on September 26 against the RSF in large parts of Khartoum and Bahri cities.
A military source, who spoke on condition of anonymity, told Xinhua on Tuesday that "the military operation is proceeding as planned."
"The SAF has made significant advancement south and southwest of Khartoum ... besides its advancement in east Khartoum areas," he added, while noting that the RSF still controls about 70 percent of the city.
In Bahri city, north of Khartoum, the Sudanese army has controlled the northwestern part, including the strategic Al-Halfaya neighborhood and its main bridge linking Bahri and Omdurman cities, the eyewitnesses said.
In Sinnar state, the SAF said in a statement that, after recapturing the state's strategic areas of Jebel Moya, Al-Dinder and Al-Suki, its units have managed to secure the road linking the cities.
Coinciding with the escalating military confrontations, a wave of defections emerged within the RSF. On October 20, its commander in central Sudan, Abu Aqla Keikel, surrendered himself and his forces to the SAF, followed by the defection of five advisors to the RSF's commander, Mohamed Hamdan Dagalo, on October 25.
"The defections constituted a painful blow to the RSF, especially its commander in central Sudan," Abdul-Rahim Al-Sunni, a Sudanese political analyst, told Xinhua news agency.
"In reaction to Keikel's defection, the RSF is now carrying out what resembles retaliatory campaigns in eastern Gezira region," he said.
The escalating military confrontations are leading to increasingly severe humanitarian crises. The International Organization for Migration (IOM) reported on Tuesday that over 14 million civilians have been displaced from their homes since the conflict in Sudan began.
"The (internal) displacement number has hit 11 million. That's up 200,000 just since September," IOM Director-General Amy Pope said in a statement.
"Another 3.1 million people have traveled across borders to flee the fighting. In total, nearly 30 percent of Sudan's population has been displaced," she added.
Pope described the situation in Sudan as "catastrophic," noting "the suffering is growing by the day" and that "almost 25 million people are now requiring assistance."
The IOM chief highlighted the cost of this displacement crisis, calling for "the guns in Sudan to fall silent."
Sudan has been ravaged by the deadly conflict between the SAF and the RSF since mid-April 2023. According to a situation report issued by the Armed Conflict Location and Event Data Project on October 14, the conflict has resulted in more than 24,850 deaths.