They cannot play, sleep or attend school. Increasingly, they cannot eat. Injury or illness could be fatal. Many just huddle with their parents in windowless underground shelters — which offer no protection from the powerful bombs that have turned east Aleppo into a kill zone.

Among the roughly 250,000 people trapped in the insurgent redoubt of the divided northern Syrian city are 100,000 children, the most vulnerable victims of intensified bombings by Syrian forces and their Russian allies.

Though the world is jolted periodically by the suffering of children in the Syria conflict — the photographs of Alan Kurdi’s drowned body and Omran Daqneesh’s bloodied face are prime examples — dead and traumatized children are increasingly common.

The routine in east Aleppo, where shellshocked children are exhumed from rubble and left writhing in bloody clothes on dirty hospital gurneys, is a confluence of Syria’s young population, failed diplomacy and the reality of a war that appears to be worsening after more than five years.

‘The Worst We Have Seen’

“They’re trapped, and they have no way of escaping,” said Alun McDonald, a spokesman for the Middle East operations of Save the Children, the international charity. “That’s one reason we’re seeing such big numbers of child casualties.”

The people living in besieged rebel-held areas of Aleppo have shown a high level of resilience, moving schools and hospitals underground for protection. So too, life has continued on the government-held western side of the city, where, according to the Syrian Observatory for Human Rights, 49 children were killed by rebel mortar fire in July alone.

But lately on the eastern side, Mr. McDonald said, “the bombing has become so intense, with such high-powered bombs, that even underground shelters aren’t safe anymore.”

Save the Children has said that at several hospitals and ambulance centers it supports in eastern Aleppo, half of the casualties have been children since the bombings escalated after the collapse of a short-lived cease-fire last week.

The battle for control of Aleppo appeared to intensify on Tuesday. Pro-government forces stepped up a new ground offensive, attacking from four directions and advancing in a central area near the city’s ancient citadel, further squeezing the insurgent-held areas.

It signifies a new determination on the part of the government and its allies to retake all of the city, but the battle could be long and grinding and take months or even years, international officials warned. Even with militia allies from Iraq, Afghanistan, Iran, and the Lebanese group Hezbollah, the government has not in the past quickly taken territory and managed to hold it.

Hanaa Singer, the Unicef representative in Syria, said precise numbers of child casualties in east Aleppo had yet to be determined. Nonetheless, she said by telephone from Damascus, “it’s definitely the worst we have seen for children.”

Just a few weeks ago, Ms. Singer said, Unicef planned to publicize how east Aleppo children were enrolled to go back to school, with photos of students walking to class past piles of rubble. That plan was scrapped.

“Children are not going to school now,” she said.

Dire Shortages

The proportion of children among east Aleppo’s trapped inhabitants is in line with the population of Syria or other countries in the Middle East with large numbers of children and people younger than 25.

But the proportion of children who have been killed or wounded in east Aleppo does appear to be higher than in other recent Middle East conflicts, according to Save the Children. In the first year of the war in Yemen, for example, about 28 percent of the civilians killed were children. In the 2014 Gaza war, the United Nations has estimated 35 percent of civilians killed were children.

Children in the besieged parts of Aleppo also face dire food and medicine shortages. Surgery and blood transfusions required for treating bomb wounds are, by many accounts, practically impossible now. Medical workers have left children to die on hospital floors for lack of supplies.

Aid groups estimate that there are only 35 doctors remaining in East Aleppo — one for every 7,143 people, assuming a population of 250,000 people. By comparison, in New York — which has the worst doctor-patient ratio of any American city — it is one for every 912 people. However, some groups say the population of eastern Aleppo is much lower, in the tens of thousands.

Nowhere to Go

With hundreds of thousands of people killed in Syria since the start of the war in 2011, and half the population displaced, that anyone is even still inhabiting east Aleppo, much less raising children there, may seem surprising.

Civil defense workers said many families, mistrustful of government offers of safe passage before the bombing intensified, had elected to stay. The government says rebels are preventing people from leaving. Others said the residents of east Aleppo — like many other Syrians — are simply reluctant to abandon their homes and properties even if they could leave.

“They don’t want to be refugees,” Ms. Singer said. “It’s their land, they’re very passionate about their houses. They say, ‘This is my house, my land.’”

Powerful, Random and Deliberate

Unlike in some other smaller-scale sieges of recalcitrant cities in Syria, the Syrian government forces and Russian military have begun dropping extraordinarily potent and not terribly precise “bunker buster” bombs which can obliterate underground shelters, residents and aid workers say.

Residents of east Aleppo have also reported the use of incendiary cluster munitions — bombs that contain hundreds of small bomblets that explode and ignite over a wide area, setting entire neighborhoods aflame.

Ben Goodlad, the principal weapons analyst at IHS Aerospace, Defense and Security, said in a report that the use of the incendiary munitions alone would appear to violate weapons conventions that ban their use in civilian population centers.

The indiscriminate nature of the bombings appears to be of little concern to President Bashar al-Assad’s government and its Russian allies, who have brushed aside Western accusations of war crimes and made it clear that they intend to retake east Aleppo regardless of the casualties and destruction.

Hannah Stoddart, director of advocacy and communications for War Child, a charity based in London, said Mr. Assad’s government had violated international law by targeting “built-up areas, schools and hospitals, where there’s a much higher chance that children will be hit.”

“On top of that, aid access is being blocked,” she said in a statement. “So if children aren’t killed or injured, they are at risk of starvation.”

Ammar al-Salmo, who leads the east Aleppo unit of the White Helmets, a civil defense group, said in a WhatsApp call that the government’s tactics “bring terror into civilians’ hearts and make it hard for rescuers to help evacuate casualties.”

The bombings, he said, have been random and irregular.

“Sometimes in the middle of the night, sometimes in the early morning so people cannot predict,” he said. “It’s is a revenge campaign against the people who decided to stay in Aleppo.”

Anne Barnard and Hwaida Saad contributed reporting from Beirut, Lebanon, and Karam Shoumali from Istanbul.