July was the bloodiest month in Baghdad's modern history - in all, 1,100 bodies were brought to the city's mortuary; executed for the most part, eviscerated, stabbed, bludgeoned, tortured to death. The figure is secret.

We are not supposed to know that the Iraqi capital's death toll last month was only 700 short of the total American fatalities in Iraq since April of 2003. Of the dead, 963 were men - many with their hands bound, their eyes taped and bullets in their heads - and 137 women. The statistics are as shameful as they are horrifying. For these are the men and women we supposedly came to "liberate" - and about whose fate we do not care.

The figures for this month cannot, of course, yet be calculated. But last Sunday, the mortuary received the bodies of 36 men and women, all killed by violence. By 8am on Monday, nine more human remains had been received. By midday, the figure had reached 25.

"I consider this a quiet day," one of the mortuary officials said to me as we stood close to the dead. So in just 36 hours - from dawn on Sunday to midday on Monday, 62 Baghdad civilians had been killed. No Western official, no Iraqi government minister, no civil servant, no press release from the authorities, no newspaper, mentioned this terrible statistic. The dead of Iraq - as they have from the beginning of our illegal invasion - were simply written out of the script. Officially they do not exist.

Thus there has been no disclosure of the fact that in July 2003 - three months after the invasion - 700 corpses were brought to the mortuary in Baghdad. In July of 2004, this rose to around 800. The mortuary records the violent death toll for June of this year as 879 - 764 of them male, 115 female. Of the men, 480 had been killed by firearms, along with 25 of the women. By comparison, equivalent figures for July 1997, 1998 and 1999 were all below 200.

Between 10 and 20 per cent of all bodies are never identified - the medical authorities have had to bury 500 of them since January of this year, unidentified and unclaimed. In many cases, the remains have been shattered by explosions - possibly by suicide bombers - or by deliberate disfigurement by their killers.

Mortuary officials have been appalled at the sadism visited on the victims. "We have many who have obviously been tortured - mostly men," one said. "They have terrible burn marks on hands and feet and other parts of their bodies. Many have their hands fastened behind their backs with handcuffs and their eyes have been bound with Sellotape. Then they have been shot in the head - in the back of the head, the face, the eyes. These are executions."

While Saddam's regime visited death by official execution upon its opponents, the scale of anarchy now existing in Baghdad, Mosul, Basra and other cities is unprecedented. "The July figures are the largest ever recorded in the history of the Baghdad Medical Institute," a senior member of the management told The Independent.

It is clear that death squads are roaming the streets of a city which is supposed to be under the control of the US military and the American-supported, elected government of Ibrahim al-Jaafari. Never in recent history has such anarchy been let loose on the civilians of this city - yet the Western and Iraqi authorities show no interest in disclosing the details. The writing of the new constitution - or the failure to complete it - now occupies the time of Western diplomats and journalists. The dead, it seems, do not count.

But they should. Most are between 15 and 44 - the youth of Iraq - and, if extrapolated across the country, Baghdad's 1,100 dead of last month must bring Iraq's minimum monthly casualty toll in July alone to 3,000 - perhaps 4,000. Over a year, this must reach a minimum of 36,000, a figure which puts the supposedly controversial statistic of 100,000 dead since the invasion into a much more realistic perspective.

There is no way of distinguishing the reasons for these thousands of violent deaths. Some men and women were shot at US checkpoints, others murdered, no doubt, by insurgents or thieves. A few listed as killed by "blunt instruments" might have been the dead of traffic accidents. Some of the women were probably the victims of "honour" killings - because male relatives suspected them of having illicit relations with the wrong man. Still others may have been murdered as collaborators. Doctors have been told that bodies brought to the mortuary by US forces should not be given post-mortem examinations (on the odd ground that the Americans will have already performed this function).

So many civilians are dying that the morgue has had to rely on volunteers from the holy city of Najaf to transport unidentified Shia Muslim dead to the central city's large graveyard for burial, their plots donated by religious institutions. "In some of the bodies, we find American bullets," a mortuary attendant told me. "But these could be American bullets fired by Iraqis. We don't know who's killing who - it's not our job to find out, but civilians are killing each other.

"We had a body here the other day and the relatives said he had been murdered because he had been a Baathist in the old regime. Then they said that his brother had been killed three or four weeks back because he was a member of the religious Shia Dawa party which was the enemy of Saddam. But this is the real story - the killing of the people. I don't want to die under a new constitution. I want security."

One of the problems in cataloguing the daily death toll is that the official radio often declines to report explosions. On Monday, the thump of a bomb in the Karada district was never officially explained. Only yesterday was it discovered that a suicide bomber had walked into a popular café, the Emir, and blown himself up, killing two policemen. Another explosion, officially said to be caused by a mortar, turned out to be a mine set off beneath a pile of watermelons as a US patrol was passing. A civilian died.

Again, there was no official account of these deaths. They were not recorded by the government nor by the occupying armies nor, of course, by the Western press. Like the bodies in the Baghdad city mortuary, they did not exist.