Story Highlights• Gen. David Petraeus: Al Qaeda in Iraq remains entrenched in parts of Baghdad
• U.S. commander says tribes in Anbar province have turned against al Qaeda
• Sectarian killings have risen in May after declining past two months
• Petraeus says tough work remains in Diyala province north of Baghdad
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BAGHDAD, Iraq (CNN) -- A new approach by American-led forces in Iraq is producing "breathtaking" improvements in security in some areas, says Gen. David Petraeus, commander of U.S. forces in the country, but al Qaeda in Iraq remains well-entrenched in some Baghdad neighborhoods.
In an exclusive interview with CNN, Petraeus said the situation in Anbar, the restive Sunni province west of the Iraqi capital, has been "truly transformed in recent months, as the Anbaris and the tribes have decided to oppose al Qaeda and fight with the coalition forces against them."
"What's taken place in Anbar is almost breathtaking," he said. "In the last several months, tribes that turned a blind eye to what al Qaeda was doing in that province are now opposing al Qaeda very vigorously. And the level of violence in Anbar has plummeted; although there clearly is still work to be done. (Watch a CNN exclusive interview with Petraeus as he discusses Iraq )
"Our strategy has always been with this new approach to determine who are the reconcilables and to separate them from the irreconcilables, the extremists," he said. (Watch how some Iraqi insurgents are turning on al Qaeda in Iraq militants)
But the picture is not consistent, Petraeus said, and the increase in U.S. forces had been more effective in some areas than others.
Tough work remains to be done in Diyala province north of Baghdad, and al Qaeda remains able to use neighborhoods around the capital to build and dispatch car bombs, he said.
He also acknowledged that after a substantial reduction in sectarian killings in the capital between January and April, the deaths have risen again in May.
The general's visit to the CNN office in Baghdad was unannounced. He said he had been visiting with Iraqi Foreign Minister Hoshyar Zebari nearby, and together they'd decided to take a walk in a part of Baghdad that is well-protected. He said it was the minister's idea to knock on CNN's door.
Petraeus said all elements connected to the increase in U.S. forces will be on the ground within two weeks, including a Marine expeditionary unit and combat aviation brigade moving toward Baghdad from Kuwait.
Asked about the infiltration of the Iraqi police by militias, Petraeus said elements of Interior Ministry forces during 2006 were "hijacked by certain militia interests in particular."
"Some of those undoubtedly remain within the force," he said. "And as we identify those individuals, and we have, and we then take action with the Ministry of Interior against them."
Gen. David Petraeus, commander of U.S. forces in Iraq, says all elements connected to the increase in American troops will be on the ground within two weeks.