The statements came a day after neighboring South Sudan announced that both generals had agreed to a cease-fire from Thursday and would name representatives to peace talks. But no date for negotiations was set, and previously truces have collapsed.

Residents of Khartoum woke up on Wednesday to heavy blasts and gunfire close to their homes, with warplanes circling the city and shelling some targets as early as 5 a.m. By noon, clashes were ongoing in neighborhoods close to the city’s international airport, one resident said.

“The Sudanese are facing a humanitarian catastrophe,” António Guterres, the U.N. secretary general, said in a speech in Nairobi, Kenya. “Hospitals destroyed. Humanitarian warehouses looted. Millions facing food insecurity.”

Even as he was fleeing, Mr. al-Hassan, the medical student, said his thoughts were with those less fortunate, including Yemeni and Syrian refugees who had been living in Sudan and could be displaced again.

Just a few weeks ago, he was working on a campaign to help refugees who had fled to Sudan from Ethiopia, he said. Now, he was on the other side, bearing a responsibility that felt much greater than his 21 years.

“I feel I have a family to protect by any means necessary,” he said. “And you don’t have guns, you don’t have power, but you use all of your people that you know and the proper way of thinking of how you evacuate your family to get here.”