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.

“Those are good trends, and we are seeing some very good numbers,” Smith said. “But obviously we have a lot of work to do, as well. Al-Qaida is still very much a threat.”

Smith says coalition forces are also focusing on militias that operate similarly to al-Qaida like those that have broken from the Jaysh al-Mahdi militia loyal to Iraqi Shiite cleric Moqtada Sadr, who ordered a cease-fire in August.

“We’re reminding really all Iraqis to think about what side they ought to be on," Smith said. "The side that Sadr’s asked them to be on, which is a peaceful side, is the right side to be on right now. And if not, we’re going to treat you like a criminal, and we’re going to hunt you down.”