Iraqi police have discovered the body of a man wearing what they say appeared to be a US military uniform.

The dead man was found floating in the Euphrates river south of Baghdad on Wednesday and had been shot in the head and chest, Captain Muthana Khalid of the Babil police said.

Police said the body had been turned over to US forces.

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"We have received the body and we will work diligently to determine if he is one of our missing soldiers, but we have not made any identification yet."

A police officer in Mussayab, 60km south of Baghdad, who declined to be named, told the Reuters news agency that the body had been found after a tip-off from residents.

Iraqi police estimated that the body had been floating in the river for at least two days.

The so-called Islamic State in Iraq, a umbrella group thought to include al-Qaeda in Iraq, has claimed it abducted the three US soldiers but has not provided any proof.

General David Petraeus, the commander of US forces in Iraq, said last Friday that he believed at least two of the three missing soldiers were still alive.