On Monday's CBS Evening News, correspondent Lara Logan relayed to viewers concerns that U.S. troops may be pulling back too quickly for the sake of security in some parts of Iraq. As Logan filed a report about the withdrawal of U.S. troops from Mosul, as part of the security arrangement supported by the Iraqi government,  the CBS News correspondent reported that some Iraqi military officers would have preferred U.S. troops stay a while longer to help in the fight against al-Qaeda.

After quoting Iraqi civilians who voiced their beliefs that things would improve after American troops left, Logan continued: "But this city is also where the main fight against al-Qaeda and their allies is still being fought. And off camera, several senior Iraqi officers told us they would have liked to have U.S. soldiers on the city streets with them for another six months."

Below is a complete transcript of the story from the Monday, June 29, CBS Evening News:

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KATIE COURIC: A big milestone today for U.S. forces in Iraq. They completed their pullout from major cities there. Tomorrow is a national holiday, and in Baghdad, the party started early. Thousands turned out for a concert by Iraqi musicians who have returned from exile. But amidst the celebration, there`s also concern. Outside Mosul, a car bomb today killed 10 people. And, in fact, throughout Iraq, more than 250 have been killed in attacks in the past week as insurgents try to undermine the government. Our chief foreign affairs correspondent Lara Logan went on one of the final patrols by U.S. troops in Mosul.

LARA LOGAN: U.S. troops have been battling al-Qaeda on the streets of Mosul for years, the fight for control of Iraq`s third largest city documented by U.S. soldiers and by insurgents. Under pressure in Baghdad last year, al-Qaeda moved north, making Mosul the most dangerous city in Iraq. But from tomorrow on, U.S. combat troops have to be out of Mosul and every other Iraqi town and city, part of a security agreement with the Iraqi government.

COLONEL GARY VOLESKY, FIRST CAVALRY DIVISION: If we`ve coordinated for a patrol, the Iraqis have said we`d like you to accompany us, and the Iraqi security force escorts don`t show up, we don`t go.

LOGAN: That means Colonel Volesky`s men will no longer be able to gather this kind of intelligence unless they`re invited by the Iraqis. Here, they`re scanning a prisoner`s iris and will add his information to a U.S. database of suspects, a vital tool in disrupting al-Qaeda. Is this area much more secure now than when you got here?

SERGEANT FIRST CLASS BRIAN SCHEMBERA, U.S. ARMY: Yes.

LOGAN: But al-Qaeda is not defeated?

SCHEMBERA: No.

LOGAN: They haven`t gone away.

SCHEMBERA: No. Will they ever?

LOGAN: On some of their last patrols in the city before the June 30th deadline, the soldiers heard from Iraqi civilians. "We expect things will get better when the Americans pull back," this man said. "We want our army here," another added. It`s clear from speaking to people here that they`ve had enough of being occupied, and they`re eager to see control of their country back in Iraqi hands. But this city is also where the main fight against al-Qaeda and their allies is still being fought. And off camera, several senior Iraqi officers told us they would have liked to have U.S. soldiers on the city streets with them for another six months. Do you think al-Qaeda will keep attacking Iraq now?

MAJOR SATAR IBRAHIM, THIRD IRAQI ARMY DIVISION: Yes. Attack Iraqi army, Iraqi government, civilian Iraqi.

LOGAN: Iraqi forces can still call on U.S. troops for help, but they`re under tremendous political pressure to show they can secure this country`s cities on their own. Lara Logan, CBS News, Mosul.

—Brad Wilmouth is a news analyst at the Media Research Center.