BAGHDAD, Iraq - The largest Shiite political coalition in Iraq on Tuesday demanded that the United States military abandon its recruitment of Sunni tribesmen into the Iraqi police force, saying some are members of "armed terrorist groups" and are killing, kidnapping and extorting under the guise of fighting Al-Qaida in Iraq.

The statement by the United Iraqi Alliance, the Shiite bloc of Prime Minister Nouri al-Maliki, is a direct rebuke to a policy that U.S. military officers hold up as one of their most important achievements over the past year.

American forces have given wide support to thousands of Sunni tribesmen across the country who have pledged to fight the insurgent group Al-Qaida in Iraq. U.S. officials call the program grass-roots reconciliation that brings disenfranchised Sunnis into the government and provides protection for their neighborhoods.

U.S. officials acknowledge that many of these recruits have been involved with various Sunni insurgent groups; expressions of antipathy toward the Iraqi security forces and government are common among them.

"We condemn and reject embracing those terrorist elements which committed the most hideous crimes against our people," the United Iraqi Alliance statement said. It also condemned "authorizing the groups to conduct security acts away from the jurisdiction of the government and without its knowledge."

It went on: "We demand that the American administration stop this adventure, which is rejected by all the sons of the people and its national political powers."

The U.S. military credits the partnerships with local Sunnis, developed in Al-Anbar province and replicated in many Sunni areas in and around Baghdad, as a primary factor in the declining violence over the past several months.

In Washington on Tuesday, Lt. Gen. Raymond Odierno, the No. 2 commander in Iraq, described these partnerships as a "success story."

"Anbar now stands as an inspiring example to the rest of the country for what is possible, as citizens come together to reject extremist behavior," Odierno said.

But some Iraqi and American officials have long expressed reservations about whether the largely Sunni Al-Anbar province could be replicated in mixed sectarian areas such as Baghdad.

"Now the problem is that the American Army has started to arm some Sunni groups . . . and give them salaries, and they've enabled them to control some mixed areas," said Humam Hamoudi, a senior Shiite leader in the coalition, in a recent interview. "This has provoked astonishment, rejection and rage."

Iraqi Vice President Tariq al-Hashimi, a Sunni, said there are insufficient American and Iraqi troops to defeat the extremists, so the local tribes provide an important supplement. He said the recruitment should continue to ensure that the recruits are accountable to the Iraqi security forces.

"At this particular moment, we need these tribes. It might be for a short period," he said in an interview. "I can't understand the fears. Frankly, it's people talking nonsense, that these tribes might turn into militiamen the next day and be a threat to the Shias and attack whomever."