But the upheaval in Syria, which has attracted a stream of Sunni extremists, has called that assumption into question.

With none of its own military forces in Iraq, the ability of the United States to train and help the Iraqis fight Al Qaeda is limited. But the United States is trying to assist on several fronts, including the sharing of intelligence to help the Iraqis uncover terrorist cells and avoid indiscriminate wide-scale dragnets that fuel Sunni resentment. During the war, Iraq’s counterterrorism forces depended heavily on American military intelligence, which used sophisticated reconnaissance systems and had the ability to locate terrorist threats by intercepting communications.

The Obama administration has also notified Congress in recent weeks that it plans to sell Iraq more than $4 billion in arms, including Stryker armored vehicles and other military systems that are suited for internal security operations.

The country’s prime minister, Nuri Kamal al-Maliki, has pressed the United States to sell Apache attack helicopters to his government. The Obama administration has been considering a number of options, leasing some Apaches to the Iraqis that they could field quickly. Some American lawmakers have been anxious about providing the helicopters for fear they might be used by Mr. Maliki to intimidate political opponents.

“They certainly would help with internal security, but they can also be used to crack down on the population.” said Nora Bensahel, a senior fellow at the Center for a New American Security. “The more the terrorist threat increases, the more likely the sale is to go through.”

The Obama administration has also been trying to broker a meeting between the Maliki government and the moderate Syrian opposition. The United States hopes such a meeting will ease the Iraq prime minister’s concerns that if President Bashar al-Assad of Syria is ousted, his government will be replaced by a hostile Sunni-dominated government on Iraq’s doorstep. It is also hoped that such a meeting would encourage Iraq to be more cooperative in pressing for a transition to a post-Assad administration.