Defense Secretary Ashton B. Carter on Wednesday defended the U.S. military’s growing training program for Iraqi troops, but he acknowledged that the government in Baghdad has provided thousands fewer recruits than expected or needed to take on the Islamic State militant group.

Carter, testifying before the House Armed Services Committee, said the United States initially envisioned 24,000 Iraqi soldiers receiving training from the U.S.-led military coalition by this fall, but only 7,000 recruits for the army and 2,000 recruits for a counterterrorism service have reported. Some of Iraq’s existing units also are manned by so-called “ghost soldiers,” personnel who are on the books and getting paid but not actually serving in the units, he added.

 [Pentagon to send 450 additional U.S. troops to Iraq]

But Carter nonetheless backed the U.S. strategy, saying the United States must continue to train Iraqi troops and will benefit by soon deploying about 450 more American service members. The plan, approved by President Obama last week, will allow for the opening of another training site at Iraq’s Taqaddum military base in Anbar province, where the Islamic State has taken control of the cities of Ramadi and Fallujah.

“The move in Taqaddum, the numbers are not as significant as the location,” Carter said. “It’s in the heart of Sunni territory, and I think it will make a big difference in the performance of the train-and-equip program in regards [to] recruiting Sunni fighters. We’re actually seeing that in the days since we established that presence there.”

Defense Secretary Ashton Carter waits to testify on Capitol Hill in Washington, Wednesday, June 17, 2015, before the House Armed Services Committee hearing on the U.S. policy and strategy in the Middle East. (AP Photo/Susan Walsh)

The plan will boost the number of American service members in Iraq to about 3,500. House committee members questioned Carter on whether the U.S. strategy is sound or if Washington must plan differently for an increasingly fractured Iraq.

“I’ve said many times before, that cow has left the barn,” said Rep. Adam Smith (D-Wash.). “Iraq is fractured. You can make a pretty powerful argument, in fact, that Iraq is no more. So when do we shift that strategy and start building the capabilities of others who will fight?”

Carter countered that the United States already has started to arm the semiautonomous Kurds in northern Iraq and is now arming Sunni tribes as well.

“We do it in coordination with the Iraqi government but in a way that doesn’t delay, as it was a few months ago, that assistance to them,” he said. “But we’re still doing it through the government of Iraq because we’re still trying to support the prime minister in maintaining a decentralized but single unitary Iraqi state.”

Carter conceded that the Iraqi military’s performance so far has been mixed — a fact widely reported following the militants’ seizure of Ramadi and Mosul, where entire units dissolved under attack by militants. Whether more U.S. troops are needed in Iraq will have to be revisited after new Iraqi units are established and trained, he said.

Gen. Martin E. Dempsey, chairman of the Joint Chiefs of Staff, added that he gets “accused of being reluctant often” but believes the United States should be judicious in adding more American troops in Iraq.

“My military judgment would be that introduction of those resources should not be done on a habitual basis because we really want them to understand that this is their fight,” Dempsey said. More American troops should be reserved for “moments where it would be strategically significant, potentially — for example, an assault on Mosul.”