But the commander of U.S. forces told CNN in an interview al-Qaida remains "well-entrenched" in some parts of Baghdad. Petraeus said Anbar, a Sunni province west of the capital, has been "transformed." Tribes there are joining the coalition in opposing al-Qaida and violence has decreased, he added.

The coalition approach focuses on trying to "determine who are the reconcilables and to separate them from the extremists," he said.

However, Petraeus admits there is tough work ahead in Diyala north of Baghdad. He says al-Qaida is still capable of using neighborhoods to build and detonate car bombs and the general confirmed sectarian killings rose again in May after decreasing between January and April.

Petraeus visited the CNN bureau in Baghdad without advance notice. He had visited Iraqi Foreign Minister Hoshyar Zebari and they decided to "talk a walk" in a safe area. The minister suggested the two of them "knock on CNN's door," CNN reported.