US troops, the only power in the Iraqi capital at the time, were criticised for not protecting the museum's collection.
Donny George, the former director of the Iraq Museum, has accused them of committing "the crime of the century" by not intervening.
The Iraq Museum, which has stood at its present location since 1966, last year completed the renovation of its Islamic and Assyrian halls, thanks to a $1.1m donation and technical help from Italy.
It is also displaying artifacts from the Sumerian and Babylonian eras.
Critics warn that the museum is being reopened before adequate security and proper cataloguing of the returned items are in place, a claim the government has rejected.
The archaeological wealth of Iraq, historically known as Mesopotamia, shows some of the first evidence of complex urban life appearing within its borders around 3,000 BC.
"We want to make our museum a place which will be at the forefront of international museums," al-Maliki said, and called on archaeologists to help make Iraq "a mecca for research" into the history of mankind.
Up to 7,000 pieces are still missing, including about 40 to 50 considered of great historical importance, according to UNESCO, the UN cultural body.
Many other historical sites in Iraq were looted after Saddam was toppled from power.