It was initially feared that 170,000 items had been taken
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More than 3,000 artefacts from Iraq's national museum have been recovered after being looted, a US team has said.
But at least 10,000 others are still missing after being stolen when war broke out, the investigators said.
The head of the team, which has been working to catalogue the items for five months, said it would "take years" to track down the missing antiquities.
More than 1,700 items were returned in an amnesty with 900 seized in raids and at checkpoints, airports and borders.
Another 750 were recovered from four different countries,
which chief investigator Marine Colonel Matthew Bogdanos declined to name.
Looters attacked the museum in the days following the fall of Saddam Hussein in April.
But initial fears that 170,000 artefacts had been stolen proved unfounded.
The 13-member US team included military, immigration and customs personnel.
Col Bogdanos said: "The reality is that after five months... we still do not have a complete inventory of precisely what is
missing."
He blamed the size of the collection and an outdated catalogue system used before the war.
Expert knowledge
Among the stolen items were a statue from 2300 BC and Roman heads of Poseidon, Apollo, Nike and Eros.
They were taken by people with expert knowledge who left copies and less valuable items, Col Bogdanos said.
And he said "numbers cannot tell the whole story".
"For example, it is impossible to quantify the loss of one of
the world's first known marble masks, in this case the mask of a Sumerian female deity or priestess from Warka."