At the main cemetery on the west side of Mosul, Iraq, kids play among the makeshift headstones sticking out of freshly dug mounds of red earth.

Some of the markers are broken slabs of concrete painted with the names of the neighborhoods where the bodies were found. "Boy and girl" reads one from the Zinjali district. In other places, a single headstone gives no indication of the multiple bodies buried underneath.

But the gravediggers remember everything.

"We dug these graves with a bulldozer. This is an entire family. One, two, three, four, five, six," says Hamid Mahmoud Hussein, counting the bodies in a single grave.

He and the others buried bodies while shooting was still going on around them.

Months of vicious fighting — the battle started in October 2016 and ended in July 2017 — left destruction so extensive that U.S. commanders compare it to the World War II battle for Stalingrad.

More than five months later, the civilian death toll is still being calculated. The Iraqi government won't talk about casualties. But figures obtained by NPR from the Mosul morgue put the number of civilians killed at over 5,000. That is likely more than the number of ISIS fighters believed to have been in Mosul and presumed dead.

Other partial estimates had pointed to high numbers of civilian deaths.

The U.N. estimates2,521 civilians were killed but cautions it has difficulty getting information.

The monitoring organization Airwars believes there are credible reports of at least 5,000 civilians killed by the coalition, Iraqi forces or ISIS. It bases much of its reporting on social media and can verify only a small percentage.

Now, Dr. Raid al-Abadi, director of the central morgue in Mosul, says 4,865 death certificates have been recorded from October 2016, when the battle started for east Mosul, until the liberation of west Mosul in July 2017.

"Those are just the bodies that have reached me," says Abadi. "We have entire families under the rubble. We still haven't pulled them out yet."

Most of the casualties were from the roughly four-month battle for west Mosul. ISIS, encircled by Iraqi forces, herded civilians deeper into the heart of the historic city to use as human shields as it made its last stand.

In addition to the recorded death certificates, Abadi says another 400 bodies are still in the morgue waiting for relatives to identify them. Many more were buried informally in gardens and communal graves as the fighting continued, and will have to be exhumed in the presence of a morgue official to obtain a death certificate.

Others yet to be counted are still buried under the rubble of collapsed buildings in Mosul's historic old section. As ISIS fighters dug in — living among captive civilians, hiding in tunnels and laying explosives — ISIS bombs, U.S. airstrikes and Iraqi mortars and artillery destroyed entire city blocks. And with them, entire families.

Abadi shows a diagram used by examiners to mark wounds in the reports listing causes of death. In a single day, he says, 172 bodies were brought from west Mosul's Zinjali neighborhood — civilians gunned down by ISIS as they tried to escape.

But that's not how most people died, he says.

"It was the destruction by the airstrikes that was the main cause," he says. "These houses in the Old City were completely destroyed. Damned ISIS was shooting one or two bullets and the airstrikes destroyed the whole neighborhood."

U.S. military officials did not respond to requests for comment on morgue figures.

During the battle, U.S. and Iraqi military commanders said they were doing their best to protect civilians. The militants used suicide bombers and drones, and moved in and out of tunnels knocked through walls. As ISIS killed more Iraqi troops, coalition airstrikes intensified.

Data given to Airwars by the U.S. military's central command shows 29,000 munitions — including bombs, rockets and artillery — were launched in support of Iraqi security forces in Mosul. They included more than 5,000 munitions dropped in March alone in a small section of the city.

U.S. military officials had estimated there were 3,000 to 5,000 ISIS fighters in Mosul at the start of the Mosul operation. In March, as the assault on west Mosul began, Lt. Gen. Stephen Townsend, commander of the combined joint task force, said he believed there were just 2,000 ISIS fighters isolated there.

As the fighting dragged on, Iraqi aircraft dropped leaflets warning civilians to stay indoors. But Iraqi and U.S. military commanders say they didn't know that the buildings ISIS was firing from had so many civilians inside.

Iraqi security forces also paid a huge toll. The Iraqi government doesn't release casualty figures. But U.S. officials have said 10,000 Iraqi security forces were killed around the country in the three-year battle against ISIS.

More than 1,500 of them, including hundreds of U.S.-trained Iraqi special forces, are believed to have been killed in fighting in Mosul. Many were killed in ISIS bombings in the street fighting needed to avoid even more civilian casualties in the densely packed city.

"One of the complaints about the battle was it went on so long," says Chris Woods, director of Airwars. "It would have taken a lot less time if Iraqi forces had not taken so much care in extracting as many civilians as they did."

Up a darkened staircase past ruined medical equipment and boxes of ISIS documents destined for the trash, west Mosul hospital director Dr. Hassan Zgyr sits in an office trying to get the hospital running again.

Zgyr was head of surgery under the ISIS occupation, and for almost the entire duration of the battle. Most of the civilian casualties he saw were women, children and the elderly. He says older boys and young men had a better chance of saving themselves.

Before 2003, Zgyr was an Iraqi army general. But he'd seen nothing like the civilian casualties streaming into his hospital this year.

"It is like a film passing in front of my eyes," he says, pausing as he tears up and then apologizes. "Somebody would bring all of his family and he would say, 'This is my wife, this is my older sister, this is my eldest daughter.' And he would count them and the only one alive is him. All the family, maybe seven — are gone."

He says most of the victims died when houses collapsed around them.

UK-based Airwars believes between 1,022 and 1,524 civilians were killed in airstrikes launched by the U.S. and its coalition allies in and around Mosul. The coalition defines airstrikes as all aircraft-launched attacks as well as rocket-propelled and ground-based artillery.

In May, Defense Secretary James Mattis described the fighting in Mosul and the Syrian city of Raqqa as a "more aggressive phase" in the battle against ISIS. Instead of attrition, where command and control and supply lines were cut, the military was using "annihilation tactics," he said.

But American military commanders deny they loosened the rules of engagement.

Neither the U.S. military nor independent monitoring organizations like Airwars or Iraq Body Count, also an independently run nonprofit group based in the UK, have conducted consistent investigations using personnel on the ground.

Although the U.S.-led coalition is believed to have fired the vast majority of munitions, the absence of information on Iraqi military attacks makes it difficult to determine who is responsible for many of the casualties.

"There are thousands of deaths of civilians in Mosul that presently cannot be attributed to any one party in Mosul," says Woods from Airwars. "I think that's a great shame, because we very much need to understand who did what right, who did what wrong and where the particular risks to civilians came from."

The original battle plan left a corridor to the west of Mosul for civilians, but would have also allowed ISIS fighters to flee, according to Iraqi military commanders at the time.

Iranian-backed paramilitary forces nominally under the command of the Iraqi government moved in from the edge of Mosul to the Syrian border. That positioning of forces cut off any escape for civilians, as well as ISIS.

"There were coalition planes — F16s and Apache helicopters — and then ISIS was launching mortars and the people were in the middle," says Hussein, a gravedigger at the Mam'oun cemetery in west Mosul.

He and other gravediggers buried more than 1,000 civilians killed in the battle. They say the survivors who dropped off bodies told them most of them died when the houses they were hiding in collapsed in airstrikes.

One grave is topped with a concrete slab, with names spray-painted in red: Badawiya and Abed. Hussein, who buried them, says Badawiya was 15 and her brother Abed, 6. When the house they were in tumbled down, the girl had her arms wrapped around her brother to protect him.

"We tried to separate them," Hussein says, "but we couldn't. We buried them together."

There is the grave of an 80-year-old man who starved to death after ISIS was surrounded and food couldn't get through to civilians.

As we walk through the cemetery, a surveillance plane flies overhead. It doesn't have the Iraqi flag of national military forces. The gravediggers identify it as belonging to the coalition.

A group of neighborhood children playing in the cemetery start up a chant in English: "America no, America no."

There is a new generation growing up believing the United States kills civilians.

Tareq Fathi, one of the gravediggers who is in his 20s, points out a policeman whose mother he says was killed by U.S. forces in 2003.

"America doesn't like peace," he says.

On the grounds of the Mosul hospital, Iraqis crowd into a tiny office to get death certificates.

"Can you help me? I want to know how to get my son's body," one woman asks the morgue administrator.

Her son was 20 and was buried near where he was killed in a mortar attack. To have him registered as dead, she will need to have him exhumed with an inspector present.

"I'm worried the bulldozers will come and I won't be able to find him anymore," she says.

The administrator, Adel Ahmed Ibrahim, had so far received 1,410 bodies retrieved by civil defense forces from the ruins of west Mosul and was updating the list every day.

His records don't break down numbers of the dead by sex or age. But as he reads the dates of birth of random entries, it is clear that many of the victims were children — some as young as a year old.

Most of the Old City of west Mosul, which suffered the worst of the damage, is still off-limits to residents. Some buildings are still piles of rubble with both explosives and bodies underneath.

In western Mosul, civil defense workers have retrieved the bodies of civilians from the ruins for three years now without being paid by the Iraqi government. They say perhaps 90 percent of them have been recovered.

On a recent day, at civil defense headquarters, families were still coming in trying to retrieve the remains of their loved ones.

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