The National Museum of Iraq is now a sorry sight. The rusting gates are shut to the public, inside layers of dust lie across the 28 galleries empty of everything except a dozen ancient statues which are just too vast to move.

More than two and half years after the ransacking of the museum by a mob following the "liberation" of Baghdad by US troops, almost 10,000 items, including some of the most precious treasures of antiquity in the world, are still missing.

Meanwhile, widespread and systematic looting of Sumerian, Assyrian and Babylonian architectural sites across the country has resulted in the heritage of Mesopotamia, the cradle of human civilisation, continuing to disappear.

The ferocious violence in Iraq, after President George Bush officially declared a victorious conclusion to the war, has meant that US forces and their Iraqi allies do not have the time or manpower to look for either the stolen museum pieces or to protect the sites scattered around Iraq.

International law agencies are supposedly chasing the ransacked items from the museum. But the man who was tasked by the US government with tracking down the looted artefacts claims that there was never any effective liaison and investigators had to depend on temporary, ad-hoc arrangements to carry on the pursuit of highly sophisticated gangs of smugglers.

Matthew Bogdanos, a colonel in US Marines reserves, who worked as a Manhattan prosecutor, has written of his experience while he was in charge of the mission in a book, Thieves of Baghdad. He said "There is no co-ordination. It's based on personal relationships, and when it works, it's a surprise."

He said he found that many Western governments were slow to help and Interpol, the ideal candidate to facilitate a global investigation, was "unwilling or unable" to do so. "I couldn't seem to convince them that this was a worldwide problem that needs immediate resolution."

Col Bogdanos also stressed that architectural heritage is being stripped away even now. "When Saddam found looters, he killed them. We told the Iraqis right away that we weren't going to fly helicopters over the sites and start shooting people."

After Col Bogdanos left his post in December 2003, the operation devolved to a myriad organisations including the cylinder-seal department of Chicago's Oriental Institute, the Iraqi State Board of Antiquities and Heritage, Interpol and the FBI. With an insurgency raging around them, US military sources say they are hamstrung and in no position to carry out art investigations.

An American officer in Baghdad remarked: "This does not even come into the equation at the moment. When we have the time off from suicide bombings, from rockets and mortars then we will start playing Indiana Jones. That may sound bad but those are the facts of life in Iraq."

Of a list Col Bogdanos compiled of the 40 most valuable stolen artefacts from the museum looting, 25 still remain unaccounted for and there are no strong leads as to where they are. They include such priceless items as the Sumerian black statue of Eannatum, one of the earliest royal sculptures to bear an inscription; the lifesize head of the goddess of victory, from Hatra; and a gold and ivory plaque of a lioness attacking a Nubian. The most acute losses are pieces which are just too famous to be offered again in the black market. Instead, say investigators, they have already been placed with hugely wealthy collectors who can only lock them away.

Professor Zainab Bahrani, am ancient near eastern historian at Columbia University in the US, is one of a shrinking number of specialists who are attempting to track the stolen heritage. He said: "You are never going to see these in a gallery. No art dealer would ever touch them, because they are just too well known. We are talking about a black market. These pieces will never again see the light of day."

Referring to the black statue of Eannatum, he continued: "I teach about it all the time. I explain why it is so important. But in the back of my mind I'm thinking 'it's gone... it's gone'."

Iraq's National Museum was established by the traveller and writer, Gertrude Bell, and opened shortly before her death in 1926. It was shut down during the first Gulf War and not reopened until April 2000. Because of the British connection, the exhibits had always been labelled in English as well as Arabic.

The remaining treasures have been locked away in underground vaults, along with a few pieces which have been recovered in Iraq. Guards with Kalashnikovs stand on the parched garden at the front of a building with flaking yellow paint. Mudhar al-Zuhairi, one of the senior managers, said: "Of course we are angry about what happened. It is a history which was stolen. But it was not just the history of Iraq, but the history of the world. We are still missing thousands of pieces and there is no information about where they are."

Asked when the museum would reopen, Mr al-Zuhairi burst into laughter. "Do you not see what is going on outside? We don't want to lose the pieces we have gathered in the past two years. Some of the pieces we have found are broken. We haven't the expertise to repair them here, but perhaps that can be done in the future. If we open the doors again, then there is a good chance that the place will get looted again. The security situation is simply not good enough. With elections coming things might improve and we shall consider the matter in the future.

"We also don't feel that even if we open up we are going to get that many visitors. People are too worried about their day-to-day safety to think about coming to the museum. This place should have been better protected when the looting took place in the first place."

The US administration faced international condemnation for doing nothing to protect the museum during the anarchic aftermath of the fall of Baghdad while quickly safeguarding the oil ministry. Two months before the invasion a group of experts warned the Pentagon about the dangers of looting following the conflict. The Geneva Convention requires an occupying force to safeguard cultural facilities and the then Secretary of State, Colin Powell, had said: "The US understands its obligations and will be taking a leading role with respect to antiquities in general but this museum in particular."

Dr Donny George, the director of research for the Board of Antiquities in Iraq, went to the Palestine Hotel, where US marines had set up headquarters, to plead for troops to protect the museum but none were sent for another three days.

Afterwards, the Defence Secretary, Donald Rumsfeld, who described the days of looting and arson in the Iraqi capital as "untidiness", said of the sacking of the National Museum: "To try to pass off the fact of that unfortunate activity to a deficit in the war plan strikes me as a stretch." And General Richard Myers, the chairman of the Joint Chiefs of Staff, said: "When some of the looting was going on, people were being killed, people were being wounded. It's as much as anything a matter of priorities."

Dr Irving Finkel, of the British Museum in London, said the looting was "entirely predictable and could easily have been stopped". Martin Sullivan, the presidential advisor on cultural property, and the State Department cultural advisor, Gary Vikan, both resigned in protest.

Some of the famous treasures have since been found. They include the Sumerian vase of Warka, the mask of Warka and a bronze Assyrian wheeled firebox. The Akkadian Bassetki statue, of a boy cast in copper, was discovered in November 2003 at the bottom of a cesspool in Baghdad. Five months earlier, the renowned treasures of Nimrud - including jewellery and ceremonial utensils - had been recovered from a secret vault in Iraq's Central Bank.

Along with the famous artefacts stolen during the ransacking, around 8,000 smaller items were taken from the museum's basement in what is seen as an "inside job". Thieves with access to keys went through storerooms containing pendants, amulets, brooches and more than 5,000 Mesopotamian cylinder seals. The collection of seals, says Col Bogdanos, could have fitted into a rucksack, and the museum numbers written in indelible ink would act as authentication of their value in the black market.

Eight of the seals were handed over to the FBI by a returning US marine, and a journalist, Joseph Braude, was arrested at New York's JFK airport with three others. He was sentenced to six months of house arrest and two years of probation.

Some of the smaller stolen items have surfaced in Britain, the US, Jordan, Switzerland, Japan and even on eBay, which offered 7,000-year-old artefacts at bargain prices. Some were returned after promises of rewards and amnesty. Rashid Ibrahim Abbas, who worked in a team created to recover the treasures, said: "The situation has now changed dramatically. One simply cannot go out and about meeting people who can lead you to the stolen items.

"There is no incentive in people taking up offers of amnesty because there is little the Americans and the Iraqi government can do to you if you ignore it, and just keep these very valuable things. Nowadays, you are very much more likely to get paid rewards for handing in weapons than handing in things stolen from the museums."

A far fewer number than expected have also surfaced on the international market. This is said to be partly due to the 2003 Sanctions Order imposed by Britain, which puts the burden of proof that an item is not stolen on the dealer. The US has also maintained sanctions on Iraq when it comes to cultural property. William Weber, of the London-based Art Loss Register, said: "The items which are coming into the market are much better provenanced. Dealers have to be very careful with this material."

The archaeologist Elizabeth Stone, of Stony Brook University in New York, said: "Somewhere there must be warehouses that are bulging at the seams because this stuff isn't showing up in the market. The people who are storing it are perhaps long-term family firms of antiquities dealers. They may be assuming that if it's not this generation then it's the next generation that's going to reap the profits."

In the meantime, she says, they are also flooding into the unregulated markets of the Gulf states where Mesopotamian antiquities are fetching very high prices.

However, even if the criminal gangs are hanging on to their artefacts, they are not abstaining from the looting process going on currently. A recent study of satellite photographs of well-known sites in southern Iraq shows, said Dr Stone, "holes denser than Swiss cheese".