The U.S. military, which just days ago completed its latest troop buildup in Iraq, has launched a large offensive operation in several Al Qaeda strongholds around Baghdad, the top U.S. commander said Saturday.

Gen. David Petraeus said the operation began in the last 24 hours, and will put forces into key areas surrounding Baghdad that, according to intelligence, Al Qaeda is using to base some of it car bomb operations.

Petraeus, who met with U.S. Defense Secretary Robert Gates at a morning breakfast, also said that while he doesn't have all the American troops he might want, he knows he's got all he's going to get.

"There's never been a military commander in history who wouldn't like to have more of something or other — that characterizes all of us here," he told reporters traveling with Gates. "The fact is frankly that we have all that our country is going to provide us in terms of combat forces. That is really it right now."

He said the buildup of nearly 30,000 additional forces that has just been completed allowed him to launch the latest assault. The move, he said, is allowing him to send operations for the first time into "a number of areas around Baghdad, in particular to go into areas that were sanctuaries in the past of Al Qaeda."

He added, "Our job now, frankly, along with the job of our Iraqi counterparts ... is to do everything that we can with the additional forces that we have."

Underscoring the challenges ahead, Gates' arrival Friday night for his unannounced visit brought him to a city all but shut down by a security lockdown. Iraqi leaders imposed a strict curfew this week after a bombing of an important shrine north of the city.

It is Gates' fourth trip to Iraq since he took over the U.S. Defense Department last December. He was meeting with military and political leaders to assess progress, and to continue to urge the Iraqi government to move more quickly toward reconciliation and to stabilize their country.

Petraeus provided few details of the new offensive, but said he believes it will help the military make some progress in Iraq, where the war is in its fifth year and U.S. casualties have surpassed 3,500. Gates and his military leaders are under intense pressure from Congress and the American public to begin to show real progress in Iraq so that troop withdrawals can start.

There are currently about 155,000 U.S. troops in Iraq.

At the same time, Gates and U.S. Ambassador Ryan Crocker expressed the continuing frustration with the lack of political progress by the Iraqis to meet a number of benchmarks set by the U.S., including oil revenue sharing legislation and political reconciliation.

"We are pressing hard on those," said Crocker. "The Iraqi government is pressing itself. Progress has ben frustratingly slow. We will see where we are by September."

Gate also visited the al-Madain Joint Security Station Saturday morning in southeast Baghdad, traveling under tight security, and wearing body armor. His helicopter sent up a cloud of dust as it set down in the rectangular, walled station in the largely Shiite enclave of Karrada, a relatively stable area of the city.

Gates heard from both Iraqi and U.S. military officials, who talked about the effort to put as many as 60 of the security outposts in the Baghdad region. There are about 27 joint security stations, which are staffed by Iraqi police and army soldiers as well as U.S. troops. And there are about the same number of smaller combat outposts.

Col. Jeffrey Bannister, commander of the 2nd Brigade, 2nd Infantry Division which has forces at the station, said the facility was a model for Baghdad and "has a very good fusion effect amongst the Iraqis."

He added, however, that his troops have faced a lot of newer armor-piercing roadside bombs. "We are at the tip of the spear for that," he told reporters who traveled to the station with Gates.

Gates thanked the Iraqi forces there for their service and expressed sympathy for those who have been wounded and killed. "They are serving the interests of the Iraqi people," Gates said.

Gates is the third top U.S. official to travel to Baghdad this week to press the Iraqi government to move more quickly toward political reconciliation and other vital reforms that many see as critical to putting a cap on the violence.

The top U.S. commander in the Middle East, Adm. William Fallon carried that message to the Iraqis last weekend, and John Negroponte, the No. 2 State Department official, reinforced it in a visit midweek.

Gates also was cautious in his assessment of the progress in the war. He's to give Congress an update next month, and a full review in September, of how well the buildup ordered by U.S. President George W. Bush has worked.

"It remains to be seen how much progress will be made over the course of the next two or three months," Gates said, adding "There are some positive trends, there are some negative trends."