“There has been an intimate relationship between them from the beginning,” Mr. Riedel said of Al Qaeda in Mesopotamia and the senior leaders of the broader Qaeda group.

But the precise relationship between the Al Qaeda of Osama bin Laden and other groups that claim inspiration or affiliation with it is murky and opaque. While the groups share a common ideology, the Iraq-based group has enjoyed considerable autonomy. Ayman al-Zawahri, Osama bin Laden’s top deputy, questioned Mr. Zarqawi’s strategy of organizing attacks against Shiites, according to captured materials. But Mr. Zarqawi clung to his strategy of mounting sectarian attacks in an effort to foment a civil war and make the American occupation untenable.

The precise size of Al Qaeda in Mesopotamia is not known. Estimates are that it may have from a few thousand to 5,000 fighters and perhaps twice as many supporters. While the membership of the group is mostly Iraqi, the role that foreigners play is crucial.

Abu Ayyub al-Masri is an Egyptian militant who emerged as the successor of Mr. Zarqawi, who was killed near Baquba in an American airstrike last year. American military officials say that 60 to 80 foreign fighters come to Iraq each month to fight for the group, and that 80 to 90 percent of suicide attacks in Iraq have been conducted by foreign-born operatives of Al Qaeda in Mesopotamia.

At first, Al Qaeda in Mesopotamia received financing from the broader Qaeda organization, American intelligence agencies have concluded. Now, however, the Iraq-based group sustains itself through kidnapping, smuggling and criminal activities and some foreign contributions.

With the Shiite militias having taken a lower profile since the troop increase began, and with Al Qaeda in Mesopotamia embarking on its own sort of countersurge, a main focus of the American military operation is to deprive the group of its strongholds in the areas surrounding Baghdad — and thus curtail its ability to carry out spectacular casualty-inducing attacks in the Iraqi capital.

The heated debate over Iraq has spilled over to Al Qaeda in Mesopotamia as well. Mr. Bush has played up the group, talking about it as if it is on a par with the perpetrators of the Sept. 11 attacks. War critics have often played down the significance of the group despite its gruesome record of suicide attacks and its widely suspected role in destroying a Shiite shrine in Samarra in February 2006 that set Iraq on the road to civil war.