Dr. Omar, the last neurosurgeon in eastern Aleppo, who declined to provide his full name out of fear for his safety, sounded desperate when reached at the height of the bombing on Friday.
“We no longer have hospitals to operate in,” he said. “You can’t imagine what it’s like living in Aleppo right now. It feels like we are living in hell. Our neighborhoods are in flames, and bombs are raining down from the sky. We urgently call on the international community to send help.”
Humanitarian agencies have described the attacks on health care facilities as deliberate.
The rebel-held area of the city is surrounded by government forces and has already run out of most food rations, medicines, bandages and fuel. It has little water.
“The regime is trying to cut off the city,” said Abu Roma, who uses a nom de guerre and is a rebel commander with the Zinki group, which opposes President Bashar al-Assad of Syria.
“I would say the worst scenario is that we will be martyrs,” he said, referring to all those remaining in the rebel-held area.
Aleppo, the country’s largest city, has been divided since 2012, but the situation became markedly worse over the summer. In recent weeks, there had been a rare respite from airstrikes on rebel-held districts, but that ended last week.
Now it appears to both fighters and civilians that the Syrian government has resolved to press forward regardless of the humanitarian cost, and to gamble that Western countries, particularly the United States, will not stop them. President Obama has never been keen on military action in Syria, and the incoming American president, Donald J. Trump, is more sympathetic to Russia, which has allied with the Syrian government.
“Aleppo is the pivot,” said Joost Hiltermann, the Middle East and North Africa program director for the International Crisis Group.
Although the government might like to reclaim all of the areas where it has lost control, Russia and Iran, another ally, are less interested, Mr. Hiltermann said.
“But they all agree on Aleppo,” he said. “It is too big to let go, and the interregnum in the United States is a good chance to press their advantage,” he said.
As always in the long-running Syria conflict, the sheer numbers of the dead and wounded and the scale of misery and destruction fast eclipses what is imaginable, and each individual story recedes. But the snapshots from the past few days in rebel-held Aleppo have been deeply disturbing.
A video circulating on social media, which was taken by Al Jazeera during the bombing at the children’s hospital, showed children being treated with oxygen masks after an alleged chlorine gas attack elsewhere in the city.
Al Jazeera captured footage of nurses taking premature infants, whom they could balance in one hand, out of incubators as clouds of dust from the bombing rose around them. One nurse hugged another as they held tiny infants in their arms. The babies were carried to a basement shelter and placed together under a blanket.
In one shot, a father cried out for his small son. “I’ve lost everything, oh, Ahmad,” he said. “I’ve lost everything, you are my life.”
For now, the only remaining medical services have gone underground or into people’s homes, said Mohamed Kahil, the head of the forensic facility in the rebel-held area of the city. “Hospitals have moved to basements, to streets, to houses,” he said.
“The medics and staff are still functioning with high energy, but under harsh conditions,” he said.
Four medics were killed in the five days since intensive bombing resumed, said Mohamed al-Ahmad, a radiology nurse in Aleppo reached on social media.
As the latest fighting took place, Staffan de Mistura, the United Nations Special Representative for Syria, traveled to Syria to press for a suspension of the bombing on all sides; a humanitarian relief effort to help civilians get medical care, food and fuel; and a guarantee some sort of safe passage for the insurgents.
Five rebel groups active in and around Aleppo — including the powerful Islamist group Ahrar al-Sham and several groups that receive American support — said in a letter late Sunday that they supported Mr. de Mistura’s plan.
Walid al-Moallem, the Syrian foreign minister who met with Mr. de Mistura, claimed to want to help civilians in the rebel-held areas, whom the regime views as “hostages” of the insurgents, according to a report by the Syrian Arab News Agency, which is close to Mr. Assad’s government.
However, Mr. Moallem dismissed out of hand any suggestion that eastern Aleppo could be self-governing. He said that would be a “reward for the terrorists,” who he said were still shelling western Aleppo, which is held by the government. He used as an example children killed Sunday in a school there. Mr. Moallem said that 11 were killed, but that number could not be confirmed.
The Syrian Observatory for Human Rights said it had documented 13 people killed in government-held Aleppo since Thursday, among them seven children killed on Sunday. At least 64 people were killed on the rebel-held side of the city in the same time period.
Mr. Moallem also appeared to reject the idea of a humanitarian pause in the bombing unless there were guarantees “from the countries supporting terrorists,” adding that the United Nations did not have any guarantees. He was referring to the United States and some Arab countries, such as Saudi Arabia, that have backed some of the groups that oppose the government of Mr. Assad.
Although groups of fighters said they were prepared to back the United Nations plan, individual fighters did not sound ready to give up.
“We will never get along with the Alawite; we will exterminate them,” Hassan Yaacoub, an independent fighter who is not with any faction, said on WhatsApp, a messaging service, referring to the minority Muslim sect of which Mr. Assad is a member.
“From now on, I will only talk in sectarian terms,” he said. “The mask has fallen. Bye, bye Syria, bye bye one Syria; Syria is no more.”