Correction: An earlier version of this article included an incorrectly attributed quotation. It was Rep. Stephen F. Lynch (D-Mass.), not Deputy Assistant Defense Secretary Gary Motsek, who said at a House subcommittee hearing: “As bad as it is, it would be worse if we had U.S. personnel guarding convoys. The body count would be unacceptable.” This version has been corrected.

Trucking contractors who pay off the Taliban, warlords and government officials to ensure safe passage for U.S. military goods in Afghanistan do so because they believe they have no choice if they want to avoid attack, a senior military official told a congressional oversight panel Thursday.

“Some of that money, for sure, is going to the insurgency,” Brig. Gen. Stephen J. Townsend said. “I can’t quantify how much is going to attacks against us. . . . I don’t think you can completely stop it, but we’ve got to minimize it.”

Townsend and Pentagon officials told a House subcommittee that a new trucking contract, which goes into effect Friday, will decrease the level of corruption through wider competition, increased vetting and improved military oversight, along with a “code of ethics” for the contractors.

The new contract is worth about $1 billion over the next year. Under the contract it replaces, tens of millions of dollars had been diverted to “malign actors,” according to congressional and military investigators.

The officials offered no assurances that the payoffs or wider corruption can be eliminated. But they said Afghan corruption is endemic and the need to supply U.S. troops is critical.

“As bad as it is, it would be worse if we had U.S. personnel guarding convoys,” Rep. Stephen F. Lynch (D-Mass.) said. “The body count would be unacceptable.”

Nearly all of the supply convoys — which transport more than 70 percent of all food, fuel, construction material and weapons to the nearly 100,000 U.S. troops across Afghanistan — are guarded by private Afghan security companies.

Military concern over payoffs first arose more than two years ago, when U.S. army investigators estimated that the going rate for protection was $1,500 to $2,500 per truck. But the military did not launch formal investigations into the issue until congressional committees conducted their own inquiries last year.

Military investigators concluded in May that U.S. funds had flowed to criminals and insurgents through four of the eight companies that were part of the earlier contract and that six of the eight were associated with “fraudulent paperwork and behavior,” including profiteering, money laundering and kickbacks to Afghan government and police officials.

Thursday’s hearing — by the House oversight subcommittee on national security, homeland defense and foreign operations — was the first in which the Pentagon explained the new contract.

Lawmakers appeared far from satisfied. Rep. John F. Tierney (D-Mass.) said military investigations had identified more than $360 million in overall U.S. contract funds diverted to “warlords, power brokers, insurgents, and criminal patronage networks” in Afghanistan. A separate government commission had estimated this month that as much as $60 billion had been lost to waste, fraud and abuse.

“I fear that these reports are only the tip of the iceberg,” Tierney said. Asked about supply pilferage, Townsend said it was only about 1 percent overall but ran as high as 15 percent of the 1.5 million gallons of fuel per day transported under the trucking contract.

Tierney and others also questioned the military’s zeal in pursuing contract abusers. Last December, the U.S. command in Afghanistan announced that it had suspended Watan Risk Group, the major security subcontractor for trucking convoys, for diverting funds and violating weapons regulations. The action, U.S. officials said at the time, was a “signal that there is a sea change underway and that we’re very serious” about combating corruption.

Last month, however, the military overturned Watan’s debarment and that of one of Watan’s security subcontractors, Haji Ruhullah. Ruhullah, widely considered a leading warlord in southern Afghanistan, acknowledged making payoffs, but he was excused by the army’s legal department on grounds that Watan had not explained contract rules to him and that his inability to speak English prevented him from reading the rules himself.

At the hearing, Tierney also raised concerns that more than half of the 20 companies awarded the new trucking contract were subcontractors under the previous version.

Kim D. Denver, deputy assistant secretary of the Army, said that none of the companies were among those with alleged abuses.

Also on Thursday, the General Accountability Office released a report saying that the departments of Defense and State and the U.S. Agency for International Development had failed to comply with laws and agreements requiring them to keep accurate count of the number of contractors employed in Iraq and Afghanistan and of the money distributed to them.

Data compiled last year by all three had “significant limitations,” including an underreporting of “at least $4 billion in contract obligations,” the GAO said.

In Thursday’s testimony, Motsek said the Defense Department employed a total of 93,118 contractors in Afghanistan as of the third quarter of 2011, nearly half of whom were Afghan nationals. The rest were about evenly divided between U.S. citizens and citizens of some other country.