NEW YORK (CNN/Money) - The Pentagon has asked its criminal unit to investigate allegations that Halliburton Co., the oil field services company once run by Vice President Dick Cheney, overcharged the U.S. government for fuel delivered to Iraq, three U.S. lawmakers said Friday.

On Thursday, a Defense Department official said the Pentagon had asked its inspector general to investigate claims that a Halliburton subsidiary, Kellogg Brown & Root (KBR), had overcharged for fuel delivered through Kuwait for U.S. government use in Iraq.

On Friday, Sen. Joseph Lieberman, D-Conn., Sen. Henry Waxman, D-Calif., and Rep. John Dingell, D-Mich., said the Defense Department's inspector general had referred the matter to its Criminal Investigative Services unit.

According to the congressmen, the inspector general, Joseph Schmitz, decided the matter warranted a criminal investigation.

"Your staff ... indicate[d] that the nature of the referral involved matters most appropriately investigated by experienced criminal investigators, rather than civil auditors," the congressmen said in a letter to the inspector general that summarized a Thursday briefing by Schmitz's staff.

The Pentagon, however, said it hadn't yet decided how to handle the issue.

"The inspector general is still in the process of assessing the referral from the [auditor]," Lt. Col. Roseanne Lynch said. "No official decision has been made regarding this matter."

Late Friday, Leslie Phillips, Democratic communications director for the Senate Governmental Affairs Committee, acknowledged that a criminal investigation had not necessarily begun -- the criminal unit could still decide not to undertake the probe.

A spokeswoman for Halliburton, the world's No. 1 oil field services firm, said the company would "welcome a thorough review of any and all of [its] government contracts."

"As a responsible government contractor we will work with the appropriate government agency," said spokeswoman Wendy Hall.

Also on Friday afternoon, the Pentagon announced that Halliburton had won the bidding for a new $1.2 billion contract to rebuild oil infrastructure in southern Iraq, leading Democrats to protest.

"It's special treatment to reward the company with yet another contract in the face of all these unresolved questions," Sen. Waxman said in a press release.

Halliburton said the new contract should quiet critics of its first contract to repair Iraqi oil fields, which was awarded without a bidding process.

"This decision is an endorsement of the courageous work being done by Halliburton's employees in Iraq," CEO David Lesar said in a statement. "We were chosen because we were the best qualified with a proven track record of the ability to perform."

Parsons Corp., a privately held construction company based in Pasadena, Calif., won an $800 million contract to repair northern Iraqi oil fields. An Australian firm, The Worley Group, will be a major subcontractor for Parsons.

In December, a Pentagon auditor questioned whether KBR overcharged the government by up to $61 million in a deal to import fuel to Iraq through a Kuwaiti company, Altanmia Commercial Marketing Co. A preliminary draft of the audit suggested the fuel might have been imported more cheaply through Turkey or other sources.

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Shortly thereafter, the Army Corps of Engineers, which gave KBR its no-bid contract to repair Iraq's oil infrastructure, said KBR's fuel prices were "fair and reasonable" and said KBR wasn't required to get cost and price data from Altanmia.

The Army Corps of Engineers could not be reached for comment Friday. In the past, it has defended KBR's arrangement with Altanmia, saying there were too many logistical hurdles to delivering oil from Turkey, Saudi Arabia or other sources.

Halliburton has also denied any wrongdoing in the matter and repeated that denial Friday.

"KBR delivered fuel to Iraq at the best value, the best price and the best terms," Hall said.

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Democratic lawmakers have also long been critical of the Army's no-bid contract with KBR to repair Iraq's oil infrastructure, worth up to $7 billion, which so far has generated about $2.3 billion of revenue for Halliburton (HAL: up $0.64 to $27.49, Research, Estimates).

Some lawmakers have accused the Army of showing favoritism in awarding the contract, a charge the Army, Halliburton and Cheney have denied.

Lawmakers have also called for Cheney to forgo the deferred compensation he will receive from Halliburton until 2005, along with hundreds of thousands of stock options held in trust. Cheney has said these options will be given to charity if and when they become valuable.