Col. Mahmoud al-Isawi said the six men were wanted on suspicion of involvement in "murders" and "attacks" in and around Fallujah, 40 miles west of Baghdad.
Al-Isawi didn't say when the arrests were made, but said the six are suspected of planning attacks and planting explosives that killed and injured civilians and members of the Iraqi security forces.
"The group is believed to be behind many murders and attacks against the citizens and the police forces," Al-Isawi told The Associated Press on Thursday. He didn't elaborate on specific attacks the men were allegedly involved in.
Fallujah is a city in the western Anbar province that was a hotbed of Iraq's Sunni-dominated insurgency and the scene of some of the most intense U.S. fighting with militants, before becoming a model of security gains in the country.
Al-Isawi said two of the six men arrested by the Iraqi police were previously detained by American troops. He said both were held in Camp Bucca, a U.S. military base in southern Iraq.
They were suspected by U.S. troops of having links with insurgents, but were released in July for lack of evidence, al-Isawi told The AP. Last month, American officials closed Camp Bucca, the U.S. troops' largest detention site in Iraq.
Iraqi and American forces have recently freed many detainees considered no longer a threat or wrongly jailed. Some former U.S. detainees have returned to violence after the release, Iraqi security officials claim.
Iraq is struggling to handle tens of thousands of detainees held in overcrowded prisons and makeshift jails.
The daunting task of managing prisons and processing thousands, detained in the past years on suspicion of links to the Sunni-led insurgency or Shiite-dominated militias during Iraq's sectarian violence in 2006 and 2007 will intensify next year when the U.S. military turns over control of its remaining detention facilities to Iraqi authorities.