The doctors' union said that since Friday morning shells had struck near four hospitals in the North Kordofan state capital El-Obeid, killing four civilians and wounding 45.
In the South Darfur state capital Nyala, the local lawyers' union said that rocket fire had killed 16 civilians.
The Darfur region, already ravaged by brutal conflict in the early 2000s, has seen some of the worst of the violence since fighting erupted in mid-April between Sudanese rival generals vying for power.
"During an exchange of rocket fire between the army and the Rapid Support Forces (RSF), 16 civilians were killed on Friday, according to a preliminary toll," the lawyers' union said.
And at least one man was killed by a sniper, it added.
In the West Darfur capital of El Geneina, near Chad, snipers have reportedly been targeting residents from rooftops since fighting began, and tens of thousands have fled across the border.
The war, which broke out in the capital Khartoum on April 15 and spread to Darfur later that month, has left at least 3,000 dead across Sudan, according to a conservative estimate.
It pits army chief Abdel Fattah al-Burhan against his former deputy Mohamed Hamdan Daglo, commander of the paramilitary RSF.
Fighting in Darfur, an RSF stronghold, has recently concentrated around Nyala, after brutal clashes in El Geneina where the United Nations had reported atrocities.
Battles have also continued in and around Khartoum. Residents reported on Saturday the first army air strikes on villages in the Al-Jazirah state, just south of the capital.
The fertile land between the White Nile and Blue Nile rivers now hosts several hundred thousands of the estimated 3.3 million people the war has displaced.
If fighting expands into Sudan's Al-Jazirah state, they may be forced to flee again.
The humanitarian workers who support them would have to move as well, but fear the many bureaucratic challenges in relocating their operations.
Analysts say both warring sides would like to see the battlefield expand.
"The RSF has held the upper hand in Khartoum since the early days of the war, but that advantage is only growing more apparent," the International Crisis Group (ICG) think tank said.
The army on July 15 launched a major offensive in North Khartoum, flattening entire suburban neighbourhoods with air raids, "but it failed spectacularly", the ICG said.
The RSF, meanwhile, are trying to seize the main Darfur-Khartoum road to ensure a constant supply of fighters and weapons.
Both Burhan and Daglo have representatives in Saudi Arabia, where truce talks have in theory been taking place.
But on Friday, the government in Khartoum denied "any information concerning a near truce".