WASHINGTON - As President Bush and Democratic challenger John Kerry clashed in late 2004 over the direction of the Iraq war, a rising Army star joined the debate.

David H. Petraeus, then a lieutenant general and head of a new command overseeing the training and equipping of Iraq's security forces, said headway was being made.

Tens of thousands of rifles, pistols, sets of body armor, vehicles and radios, along with millions of rounds of ammunition, had been delivered to Iraqis over a three-month period, he wrote in a commentary for the Washington Post six weeks before the presidential election.

The weapons and countless pieces of other gear, paid for with tens of millions of U.S. tax dollars, were indeed flowing - but, as it turns out, not always to the right places or into the right hands.

In the rush to arm Iraqi forces against a violent insurgency, U.S. military officials did not keep good records. About 190,000 weapons were not fully accounted for, according to one audit.

The accounting failures are at the heart of a broad inquiry by the Pentagon's inspector general, sharp questions from Republicans and Democrats in Congress, and complaints from officials in Turkey who claim that pistols used in violent crimes in their country came from U.S.-funded stocks.

Retired Army Maj. Gen. Paul Eaton, who preceded Petraeus as the officer in charge of training Iraq's forces, said he expected the inspector general would find that there were too few people to handle the enormous influx of weapons and money into the country.

"One of the greatest irritants to me was watching the Pentagon cooking along at full strength while we in Iraq were running on a very thin personnel shoestring," said Eaton, a critic of the Bush administration's handling of the war.

"There have never been enough people, and there has never been enough bureaucratic support and effort to do this thing properly," Eaton said.

Peter Velz, a Pentagon official specializing in Iraq issues, said Petraeus' command was operating under "extremely difficult, spartan conditions," and was in need of more personnel experienced in contracting and materiel management.

The training command had about 900 people in 2004, according to a command spokesman, and it now has 1,100.

There is no evidence of any wrongdoing by Petraeus, now a four-star general and the American commander in Iraq. There also is no indication that he is the subject of any of the inspector general's inquiries.

In June 2004, Petraeus took over the just-formed Multinational Security Transition Command-Iraq, more commonly known by the acronym MNSTC-I (pronounced "min-sticky"). The organization's job is to train Iraqi army and police units so they are capable of operating on their own.

Petraeus has likened the experience to "building an aircraft that was already in flight."

Given the rising strength of the insurgency at the time, Petraeus felt it was more important to get weapons and ammunition to troops in the fight "than to wait for a signature on a hand receipt," Army Col. Steven Boylan, Petraeus' top spokesman, said Tuesday by e-mail.

Petraeus left the post in September 2005. Since then, audits have cited the Iraq transition command for lack of oversight.

An October 2006 audit by the special inspector general for Iraq reconstruction said there was "questionable accuracy" and "incomplete accountability" in the way MNSTC-I managed weapons.

In one case, 751 assault rifles were purchased, but there is no record of their delivery to Iraq's defense and interior ministries.

More recently, the Government Accountability Office said that, until December 2005, MNSTC-I had no centralized set of records for the shipping of weapons to Iraqi forces.

The command said 185,000 Russian-designed AK-47 rifles, 170,000 pistols, 215,000 sets of body armor, and 140,000 helmets had been issued to Iraqi troops by September 2005, according to the July GAO report.

But because of incomplete record-keeping, the command could not be certain if the Iraqis received 110,000 of the rifles or 80,000 of the pistols. More than half of the body armor and helmets also could not be tracked.