U.S. Defense officials on Thursday said combat mission in Iraq will continue through end of August, although the last U.S. combat brigade has left Iraq Wednesday night.

"Our mission still continues," Stephen Lanza, spokesman for U.S. Forces Iraq, told CBS "Early Show." "We're going to transition from combat operations to stability operations, and we're doing that as we're drawing down our forces right now to 50,000 by Sept. 1."

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"With that brigade that just left, we're roughly a little under 56,000 (troops)," Lanza said. That number, he said, will steadily decrease within the next 12 days to meet President Barack Obama's mandate.

A convoy of the 4th Stryker Brigade of the 2nd Infantry Division, the last full U.S. combat brigade in Iraq, crossed into Kuwait Wednesday night, leaving Iraq ahead of the Aug. 31 deadline, which Obama has set as the end of combat operations in Iraq. Washington said that about 50,000 U.S. troops will remain in Iraq to conduct support and training missions. The last U.S. troops will leave Iraq by the end of 2011.

Pentagon spokesman Bryan Whitman said the transition from combat mission to advise and assist won't take place overnight.

"This is not like a light switch, where one day you are doing combat operations and the next day you are doing stability operations," Whitman said. "It has been a transition that has taken place gradually over time."

Whitman said six U.S. Army brigades, plus support personnel, will work with Iraqi security forces through the end of 2011. The units are the 1st, 2nd, 3rd and 4th brigades of the 3rd Infantry Division, the 3rd Brigade of the 4th Infantry Division and the 2nd Brigade of the 25th Infantry Division.

U.S. Air Force personnel will continue to help in training the Iraqi air force, and Navy and Coast Guard personnel will continue to advise and assist Iraq's maritime forces.