The daily quoted two US military officials who said US troops had found no bodies when they arrived on the scene.
Major Richard Goldenberg, spokesman for the 42nd Infantry Division, told the Post: "I can't confirm the [Iraqi] estimate ... the insurgent forces who had fled ... were able to recover their casualties and take them with them."
On Thursday, an AFP reporter who travelled to the camp overlooking Lake Tharthar, 200km north of Baghdad, reported 30 to 40 fighters roaming its streets.
The remains of three burnt vehicles were seen on a dusty road leading to the camp in the village of Ain al-Hilwa. A few mud huts were partly destroyed and a few big craters were seen on the ground.
One of the fighters, who called himself Muhammad Amir and claimed to belong to the Secret Islamic Army, said they had never left the base.
He denied that scores of his fighters had been killed and said only 11 of his comrades perished in air strikes on the site.
Unknown numbers dead
Goldberg confirmed that Apache attack and Kiowa Warrior reconnaissance helicopters had engaged the fighters and offered support to the Iraqi commando force.
Apaches stepped in after the
commando unit came under fire
"I would tell you that somewhere between 11 and 80 lies an accurate number," he told the Post.
"We could spend years going back and forth on body counts," he said. "The important thing is the effect this has on the organised insurgency."
A spokesman for the interim Iraqi Interior Ministry said he "presumed" the reported toll was accurate.
However, he dismissed the raid on the camp as a major incident, highlighting that it was the first major Iraqi police operation with US forces acting in a supporting role only.
Local hospitals said they had received no casualties from the battle.