The military is casting doubt on Barack Obama's claim during a debate Thursday night that for U.S. troops in Afghanistan, it was "easier to get Taliban weapons" than it was to be properly equipped by their own country.

Pentagon spokesman Bryan Whitman said Friday he found the claim "hard to believe."

"Despite the degree of skill and finesse that it takes to manage a large force with the number of deployments we have going on -- and despite the stress that we have readily acknowledged on the force, one of the things we do is make sure that all of our servicemen that are going into harm's way are properly trained and equipped with the leadership they need to be successful," he said.

Obama's campaign stands by his remarks, which he made during a debate with Hillary Clinton in Austin, Texas, while explaining why he feels he is prepared to be commander-in-chief and why the decision to enter Iraq demonstrated poor judgment.

During the debate, he said he was told by an Army captain heading a rifle platoon that he was sent to Afghanistan with 15 fewer soldiers than he was supposed to have because the other troops were sent to Iraq.

"And as a consequence, they didn't have enough ammunition; they didn't have enough Humvees," Obama said. "They were actually capturing Taliban weapons, because it was easier to get Taliban weapons than it was for them to get properly equipped by our current commander-in-chief."

The Army captain Obama mentioned later told FOX News that in fact he and his platoon were fighting near the Pakistan border with only three Humvees, one of which had no doors and no roof.

The captain, who asked not to be identified, said his mounted machines guns stopped working and without the proper parts to repair them the troops were forced to scavenge for Taliban weapons. The captain said he met Obama in 2003 and later told his story to an Obama staffer.

Army spokesman John P. Boyce Jr. issued a statement saying: "Without a unit designation or time frame of deployment, it's difficult for us to verify the validity of what was told to the senator. Our soldiers deploy as complete units -- either as companies, battalions or brigades, and they do so with every soldier armed with his or her individual weapon. ... Army units and individual replacements arrive in country fully capable to conduct combat operations."

FOX News' Justin Fishel contributed to this report.