The BBC has reported that the capital's main mortuary has received 6,000 bodies since January, with the number rising each month with 1,400 in May alone.
Most of the bodies died violently and are believed to have been victims of sectarian killings. However it is widely believed that the correct figure is much higher.
The revelations come as at least nine people were killed in attacks across Iraq on Tuesday, as police discovered nine severed heads wrapped in plastic in a box used to carry fruit on the highway outside the city.
Some of the heads were blindfolded and already decomposing, indicating that the killings took place some days ago. A similarly grisly discovered of heads was made on Saturday in Baquba.
Prisoners released
Meanwhile, Iraqi Prime Minister Nouri al-Maliki has announced he will release 2,500 prisoners, in an apparent bid to boost his own authority.
The releases will start later on Wednesday, and Mr Maliki described the move as a gesture of "national reconciliation".
He said those with no clear evidence against them or anyone mistakenly detained would be freed.
However no Saddam Hussein loyalists would be allowed to leave prison. "Those who committed killings or bombings will not be released," he said.
A UN human rights report last month said that there were 28,700 detainees in Iraq, including 5,000 held by the Interior Ministry even though it should only detain people for short periods of time.
"Torture and other cruel, inhumane or degrading treatment are allegedly common practice in some facilities," it said. The move has been welcomed by the United States.
In Britain, a military court has cleared three British soldiers of killing a 15-year-old boy, who drowned in a canal in southern Iraq after the US-led invasion in March 2003.
Prosecutors claimed the boy, who was unable to swim, had been forced into the canal by the soldiers, along with three other suspected looters, a week after the official end of the Iraq war in May 2003. But the soldiers denied the charges.