"There are still clashes between army forces and the Rapid Support Forces (RSF), leaving buildings, facilities and public property destroyed," a doctors' committee said on Friday.
A coalition of civil groups said on social media it had submitted a proposal for a three-day truce to rival factions locked in a week-long battle for control, and they responded favourably.
"We welcome the positive position of the leadership of the Sudanese Armed Forces and the Rapid Support Forces," the group said, adding it would continue to work on details.
Neither force publicly said it had agreed to a ceasefire.
The RSF issued a statement that made no mention of a possible truce and condemned the military for what it said were fresh assaults.
"At this moment, when citizens are preparing to receive the first day of Eid al-Fitr, the neighbourhoods of Khartoum are waking up to the bombings of aircrafts and heavy artillery in a sweeping attack that is directly targeting residential neighbourhoods," the RSF said on Friday.
United Nations Secretary-General Antonio Guterres on Thursday appealed for a ceasefire to allow civilians to reach safety.
Thousands of civilians streamed out of the capital Khartoum as gunfire and explosions sounded on Thursday.
Large numbers also crossed into Chad to flee fighting in the western region of Darfur.
At least 350 people have been killed so far in the violent power struggle that broke out last weekend between two previously allied leaders of Sudan's ruling military junta, Sudan's army chief General Abdel Fattah al-Burhan and RSF leader General Mohamed Hamdan Dagalo.
A doctors' group separately said at least 26 people were killed and 33 were injured in El-Obeid, a city west of Khartoum, on Thursday - the eve of Eid al-Fitr which ends the Muslim fasting month of Ramadan.
Witnesses there described clashes between the army and RSF troops and widespread looting.
Guterres, speaking to reporters after meeting virtually with the heads of the African Union, the Arab League and other organisations on Thursday, said: "There was a strong consensus on condemning ongoing fighting in Sudan and calling for cessation of hostilities as an immediate priority."
Urging a three-day ceasefire, he said civilians trapped in conflict zones should be allowed to escape and seek medical treatment, food and other supplies.
The United States endorsed the ceasefire proposal.
Burhan told Al Jazeera he would support a truce on condition it allowed citizens to move freely - something he said the RSF had so far prevented.
He said he currently saw no partner for negotiations and "no other option but the military solution".
His rival Dagalo told Al Jazeera he was ready to implement a three-day truce.
Dagalo, widely known as Hemedti, has said several times he supports short ceasefires but each has quickly collapsed.
"We are talking about a humanitarian truce, we are talking about safe passages ... we are not talking about sitting down with a criminal," Dagalo said, referring to Burhan.
Burhan accused Dagalo, until last week his deputy on the council that has ruled since a coup two years ago, of "a power grab".
An alliance between the two men had mostly held since the overthrow four years ago of long-time strongman Omar al-Bashir, whose rule saw Sudan become an international pariah on the US terrorism list.
The latest violence was triggered by disagreement over an internationally backed plan to form a new civilian government.
About 10,000 to 20,000 people escaping the fighting have taken refuge in villages along the border inside Chad, UN refugee agency UNHCR said.
About a quarter of Sudan's population was facing acute hunger before the conflict but the World Food Programme halted one of its largest global operations in the country on Saturday after three workers were killed.
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