"I think it's probably going to be the summer, late summer, before you get to the point where people in Baghdad feel safe in their neighborhoods," Casey told reporters at a news conference with visiting U.S. Defense Secretary Robert Gates.
Asked how long the 21,500 extra U.S. troops are likely to be kept in Iraq, Casey replied, "I believe the projections are, late summer."
CBS News correspondent Cami McCormick reports the U.S. influx is underway, with a brigade of the 82nd Airborne that recently arrived in Baghdad already at work clearing neighborhoods in the dangerous capital city.
McCormick says additional troops are also to be sent to the restive Anbar province.
Gates' visit here — his second since replacing Defense Secretary Donald H. Rumsfeld last month — was not announced in advance. It comes as the Bush administration begins a new phase in the war including a troop buildup that has encountered widespread opposition in Congress, a reshuffling of Mideast commanders and diplomats, and intensified military pressure on Iran.
Gates immediately went into talks with U.S. commanders and their allied counterparts amid the burgeoning war policy debate in the United States.
The first group of extra troops — a brigade of the 82nd Airborne Division — has just arrived in Baghdad, and Gates said it was too early to predict how Bush's plan for quelling the sectarian violence in the capital will work. Four other brigades are to be sent to Iraq between now and May, assuming the Iraqis follow through on their commitment to bring three additional Iraqi army brigades into Baghdad and to allow raids against all illegal militias.
Asked how the Iraqi government was doing to meet its commitments, Casey said, "So far, so good."
Gates arrival in Iraq was made public hours after officials announced that U.S. and Iraqi forces had to Muqtada al-Sadr, who runs the country's most feared Shiite militia and is viewed by many Sunni's as being in cahoots with Shiite Prime Minister Nouri al-Maliki.
Casey stressed that it was too early to say with confidence how long the U.S. military will have to maintain a higher troop level in Baghdad and western Anbar province. But he sounded an optimistic note.
"You're going to see some progress gradually over the next 60 to 90 days," he said.
Casey is being replaced soon by Lt. Gen. David Petraeus, although the timing is uncertain. Casey has been nominated to become the next chief of staff of the U.S. Army, but he has not yet been confirmed in that job by the Senate.
"It will be late summer before we see the results that would cause us to make some decisions like that," Casey added, referring to the prospect of reducing the overall size of the American force, which stood at 132,000 troops at the time Bush announced he was sending reinforcements.
The troop buildup is scheduled to unfold in phases, with the full contingent of five extra brigades not in place until May.
Britain, which has the largest troop contingent among the U.S. allies, with about 7,000 soldiers in the Basra area, is planning to withdraw a large portion of them this year.
Gates said at the outset of his weeklong overseas trip that he realized the security situation in southern Iraq is different than in Baghdad, where the United States is building up its troop strength.
Gates and Casey took a cargo plane to the Tallil air base near the ancient city of Ur and about 10 miles from the southern city of Nasiriyah. They met there with commanders from several coalition countries, including Australia, Poland, Romania and Denmark.
On his first visit to Iraq after being sworn in on Dec. 18, Gates met in Baghdad with U.S. commanders and Iraqi government leaders just weeks before Bush announced his new strategy for Iraq.
A British military spokesman in Basra told reporters that no "hard evidence" had been obtained of Iranian arms, money or weapons technology entering southern Iraq, but he added, "As a gut feeling we know there is Iranian influence" here. The predominantly Shiite Muslim areas of southern Iraq have historic ties to Iran, which is a predominantly Shiite nation.
The Bush administration has accused Iran of meddling in Iraqi affairs and contributing technology and bomb-making materials for insurgents to use against U.S. and Iraqi security forces.
The British spokesman, Maj. Chris Ormond-King, also said it was possible that Basra province, which includes the city of the same name, could be turned over to full Iraqi government control by this spring. He said there is no firm timetable. Basra is Iraq's second-largest city after Baghdad.
Two of the other four provinces in southeastern Iraq that are the responsibility of the British-led multinational force were returned to full Iraqi control last year. A third, Maysan province, is due to be turned over to the Iraqis in several weeks, Ormond-King said.
Although security in southern Iraq is better than in Baghdad, the British are still having some trouble with militia influence within the Iraqi police services.
Gates' overseas tour began in London and took him to NATO headquarters in Brussels, Belgium, and to Afghanistan before he arrived in the Gulf on Wednesday.