BAGHDAD, July 9 (Reuters) - Corruption is rampant at "every level" of Prime Minister Nuri al-Maliki's government, with Iraqi graft inspectors calculating that at least $4 billion has been pilfered from state coffers, a top U.S. official said.

The Office of the Special Inspector General for Iraq Reconstruction will report to the U.S. Congress this month that corruption remains "a very huge challenge to the government of Iraq", Ginger Cruz, deputy inspector general at the oversight agency, told Reuters in an interview in Baghdad on Saturday.

"It is something that requires international cooperation. It is a very, very serious problem. Corruption is evident in every level of government ... in every one of the ministries.

"It is probably one of the biggest problems facing them," she said, singling out smuggling in the oil sector, the lifeblood of Iraq's shattered economy, as a particular problem.

Oil exports provide virtually all Iraq's government revenue and are crucial to efforts to rebuild the economy. Maliki's oil minister has vowed to crack down on the smuggling of state-subsidised oil and oil products out of Iraq.

"The government needs to create conditions through which there is increased transparency of oil revenues," Cruz said.

Washington has warned that if corruption in the oil and gas sector continues unchecked it could have devastating effects on efforts to stabilise the country.

Cruz said the inspector general of Iraq's Health Ministry, who heads a committee of all ministry inspectors general, had reported that corruption had cost the Iraqi state $4 billion.

In one of the most high-profile cases, Iraq issued arrest warrants for the former defence minister and two dozen other officials in 2005 in connection with the alleged misappropriation of more than $1 billion from state coffers.

Maliki has made tackling corruption and establishing budgetary audits a key priority of his new coalition national unity government, which is also seeking to end a three-year-old Sunni insurgency.

"We are fighting two insurgencies -- one terrorist and criminal and the other corruption," Cruz said.

BUSH PROMISES HELP

U.S. President George W. Bush has promised to help Iraq fight graft, and Cruz said U.S. officials were helping to strengthen financial management and accounting systems.

Cruz said her office, set up in January 2004, was also investigating 86 cases involving fraud by contractors, briberies and kickbacks and theft running into the millions of dollars related to Iraq's U.S.-funded reconstruction effort.

She said agents from the FBI's fraud division had recently agreed to help investigate the cases.

In the only case reported to have come before a U.S. court, an official in the former Coalition Provisional Authority (CPA) and a U.S. contractor have admitted to conspiring with several U.S. Army officers, to rig bids on rebuilding contracts.

The New York times reported on Friday that Army reserve Lieutenant Colonel Bruce Hopfengardner had offered to plead guilty to charges of bribery and money-laundering in the scheme. Cruz confirmed he was a suspect in the case.

She said investigating cases dating from the CPA, the former U.S. governing authority in Iraq, was particularly troublesome.

"We were dealing with a cash economy then, so it has been difficult to find a paper trail," she said.

But better oversight and strict controls had led to a significant decrease in the number of cases being reported.

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