BAGHDAD, Nov. 1 (UPI) -- The ability of al-Qaida to spread propaganda, recruit and gain financing for operations has been greatly diminished in Iraq, according to a U.S. commander.

Navy Rear Adm. Gregory J. Smith says al-Qaida is not defeated, but the militant group is on the run, the American Forces Press Service reported.

“We’ve taken out a significant part of their leadership," Smith said in a statement. "We’ve gone after their foreign fighter facilitation network. We’ve gone after their financial networks. And we also have gone after very heavily their propaganda network.”

Smith also says coalition forces have destroyed as much as 80 percent of al-Qaida’s media structure, which greatly hampers their ability to operate.

Additionally, some U.S. military reports are indicating a downward trend in overall violence in Iraq. But Smith cautioned that al-Qaida is still dangerous.