WASHINGTON — Al Qaeda is in Iraq to stay.

It’s not a conclusion the White House talks about much when denouncing the shadowy group, known as Al Qaeda in Iraq, that used the American invasion five years ago to develop into a major killer.

The terrorists are weakened, battered, perhaps even desperate, by most American accounts. But far from being “routed,” as Defense Secretary Gates claimed last month, they’re still there, still deadly active, and likely to remain far into the future, military and other officials say.

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Commanders and the other officials commented in a series of interviews and assessments discussing persistent violence in Iraq and intelligence judgments there and in America.

Putting the squeeze on Al Qaeda in Iraq was a primary objective of the revised American military strategy that General David Petraeus inherited when he became the top commander in Baghdad 13 months ago. The goal — largely achieved — was to minimize the group’s ability to inflame sectarian violence, which at the time was so intense that some characterized Iraq as trapped in a civil war.

However, the militants are proving they can survive even the most suffocating American military pressure.

“They are not to be underestimated. That’s one thing I’ve seen over and over,” the commander of the Army’s 1st Brigade, 3rd Infantry Division, Colonel John Charlton, said. His unit has fought Al Qaeda for the past 14 months in a portion of Anbar province that includes the provincial capital of Ramadi.

“I’m always very amazed at their ability to adapt and find new vulnerabilities,” Colonel Charlton said in a telephone interview this week from his headquarters outside of Ramadi. “They are very good at that,” even though they have largely lost the support of local citizens.

The American and Iraqi government intent is to chip away at Al Qaeda until it is reduced to “almost a nonentity,” Army Lieutenant General Ray Odierno said March 4 shortly after finishing his tour as the No. 2 American commander in Iraq. “Unfortunately with these terrorist organizations, they will always be there at some level.”

Demonstrating anew their remarkable staying power, the militants are thought to be behind attacks in recent days in Baghdad and beyond, including bombings in the capital March 7 that killed at least 68 people.

Now that American troop reinforcements are beginning to go home, General Petraeus and the Bush administration will be watching closely to see if American-trained Iraqi forces can keep up the pressure on Al Qaeda.

Al Qaeda in Iraq, which did not exist as a coherent group before American troops invaded in March 2003, probably now numbers no more than 6,000, according to American intelligence estimates. It may have been closer to 10,000-strong before the severe pummeling it took last year, when it lost its main bases of Sunni Arab support. It controls no cities but is still active in pockets through much of central and northern Iraq.

Colonel Charlton, whose unit is leaving Iraq shortly and will not be replaced by another American brigade in Anbar, said he is confident of the Iraqis’ determination not to allow Al Qaeda back into their communities.

But resilience has been a hallmark of Al Qaeda in Iraq, which emerged only after its leader, the Jordanian terrorist Abu Musab al-Zarqawi, pledged his allegiance to the leader of the global Al Qaeda network, Osama bin Laden, in October 2004. It has survived innumerable reverses in recent years, including al-Zarqawi’s death in a June 2006 American airstrike

The successor to al-Zarqawi is an Egyptian who keeps a lower public profile, Abu Ayub al-Masri.

The group’s other leadership figures also are foreigners from Arab nations including Saudi Arabia, Tunisia, Yemen, Syria, Morocco, and Libya, according to two defense officials who discussed details of the organization on condition of anonymity. The rank-and-file membership is largely Iraqi.

Hardly a day goes by that the American military command in Baghdad doesn’t announce the capture or killing of an Al Qaeda figure. Yesterday, for example, the military said troops detained four suspected terrorists northwest of Samarra while targeting an alleged foreign terrorist facilitator and associates of a media cell leader involved in Al Qaeda’s network in Anbar province.

An Al Qaeda watcher at the Combating Terrorism Center at the U.S. Military Academy, Brian Fishman, said that although Al Qaeda in Iraq lost some of its “strategic focus” after al-Zarqawi’s death, it remains a threat.

“It’s way too soon to count these guys out,” he said.

In a report to Congress this week, the Pentagon said elements of Al Qaeda in Iraq are “highly lethal” in parts of the Tigris River valley north of Baghdad and in Ninevah province in northern Iraq. And it said the group, though less effective overall, is capable of striking “across Iraq.”

That doesn’t seem to fit the description offered by a battalion commander in the 1st Infantry Division, Army Lieutenant Colonel John A. Nagl, who wrote in an opinion article in The Washington Post on March 9 that Al Qaeda in Iraq was “largely defeated.”

Certainly the group’s stated goal of establishing an Islamic fundamentalist state in Iraq has been blocked. And there is no sign that Al Qaeda is anywhere near being in position to regain momentum.

The Army commander in Ramadi, Colonel Charlton, said propaganda material from local Al Qaeda members or supporters has changed markedly in tone in recent months.

“Back in early 2007 and in 2006 you would typically see propaganda that was very boastful, very aggressive and very confident,” Colonel Charlton said. “It would say things like, ‘We’re coming to get the sheiks, we’re going to kill them all,’ that type of stuff. Lately, the propaganda is very different. It’s appealing on an ideological basis to the population — as if they realize they’ve lost the support of the people.”

But Al Qaeda isn’t going away.

The top U.S. commander in Anbar province, Marine Major General John Kelly, told reporters at the Pentagon by teleconference this week that Al Qaeda in Iraq has the wherewithal, when squeezed, to shift to other places. After being pushed out of Anbar in early 2007, the militants reasserted themselves in Baghdad. After getting hammered in the capital they slipped north, first to Diyala and more recently to the northern province of Ninevah, whose capital, Mosul, is now the scene of heavy fighting.

“Our sense is they’ll come back to where they know best,” General Kelly said, referring to Anbar.