About 6,870 works were stolen from the Iraqi Art Museum in the aftermath of the US-led invasion in 2003 which saw widespread looting across the capital.
Friends of the museum have begun to track down and return hundreds of oil paintings, watercolours, drawings and sculptures representing the work of some of Iraq's finest artists of the past two centuries.
Huda al-Nuaimi, the museum director, said: "We have managed to recover 1,130 pieces from people who bought these works in Amman and Baghdad, perhaps not knowing they were looted, and have now returned them."
Unguarded buildings in the capital were stripped by gangs of looters after Saddam's security forces were driven out by the US military, but Al-Nuaimi believes that the artworks were taken by professionals.
"The paintings were stripped from their frames and folded in a delicate and careful way," al-Nuaimi said, adding that she suspected that the thieves must have had knowledge of the collection and the layout of the gallery.
Despite this, some of the returned pieces were damaged and curators are working with experts to restore stretched canvases.
"We have managed to recover 1,130 pieces from people who bought these works in Amman and Baghdad".
Huda al-Nuaimi, director of the Iraqi Art Museum
"We've sent two of our staff to Italy for a course on how to restore works of art," she said.
Most of the stolen artworks seem to have ended up being sold privately, and they have begun to show up in collections around the region, where Iraqi officials can spot them and contact their owners.
The Qatari embassy in Jordan, for example, recently sent back five pieces by renowned Iraqi painter Faiq Hassan, the leading light in the "Pioneers Group" whose naturalistic style dominated Baghdad art in the 1950s.
The paintings had been hung in the Amman embassy after being bought in good faith, but have now been sent back to Baghdad.
The looting spree stripped museums in Baghdad and Mosul of thousands of years of historical artifacts and artworks.
Most of Iraq's art museums are struggling to recover to re-establish themselves because of a lack of funds and the sectarian violence which is gripping the country.