But there is little direct evidence to support the charge or to prove that the group is behind terrorist acts in Iraq.
Last week's detention in Oslo of Mullah Krekar, the group's founder and spiritual leader, has brought Ansar Al-Islam back into the spotlight. It's the second time in a year that Krekar has been held by Norwegian authorities. He is likely to be released soon, however, since a court has ruled that there is not enough evidence to link him to planning terror attacks in Iraq.
Krekar, born Najm al-Din Faraj Ahmad, was granted political asylum as a Kurdish refugee by Norway in 1991. But in the years since, he is known to have frequently visited Kurdistan in northern Iraq, where in 2001 he founded Ansar Al-Islam, or "Supporters of Islam."
He is still believed to be an important figure in the organization, though he denies any connection to terrorist activities.
Paul Wilkinson is a professor at the Center for the Study of Terrorism and Political Violence at St. Andrew's University in Scotland. He says the decision of the Norwegian court to free Krekar is logical.
"I can understand the Norwegian court's great difficulty on this matter because there is a lack of really crucial evidence that would be required to prove the connection," Wilkinson said.
Many others think differently.
The U.S. military believes the group is behind a series of unsolved car bombings and deadly suicide attacks in Baghdad. Last September, speaking in Oslo, U.S. Attorney General John Ashcroft called Ansar Al-Islam a "very dangerous group."
A member of the Iraqi Governing Council, Muwaffaq al-Rubay'i, agrees. In an interview with RFE/RL, he said there is no doubt that Ansar Al-Islam is an extremist group that is "adopting violence to implement its ideology."
However, al-Rubay'i admits there is only indirect evidence to support his claim. "Well, I'm not a judge. I'm not a court. But I believe there is substantial evidence -- I should say circumstantial evidence, as well -- to connect this organization to acts of terrorism in Iraq," al-Rubay'i said.
The Kurdish Sunni militant organization was created and initially based in northern Iraq, northeast of the town of Halabjah in Sulaimaniyah Province, bordering Iran. The group split from the Islamic Movement of Kurdistan, the third-most significant political force in Iraqi Kurdistan at the time. Ansar Al-Islam reportedly has less than 1,000 members.
Ansar Al-Islam's ideology entails a literal interpretation of the Koran and advocates a return to the proclaimed purity of the early Islamic community.
Representatives of the New York-based rights group Human Rights Watch (HRW) visited Ansar Al-Islam camps in 2002. In a report, HRW says that, in its early days, the group issued decrees ordering women to wear veils, men to grow beards, the segregation of the sexes, banning music, and barring women from education and employment. The group also said it favored Islamic punishments -- amputations and floggings -- sometimes to the death -- for offenses such as theft, the consumption of alcohol, and adultery.
Human Rights Watch says the group is responsible for numerous human right violations -- such as illegal detentions, the killing of combatants after surrender, and torture.
Ansar Al-Islam says it seeks to offer an alternative to "secular" Kurdish political parties, such as the Patriotic Union of Kurdistan (PUK) and the Kurdish Democratic Party. In the 1990s, numerous clashes were reported between PUK forces, which controlled the region, and Ansar al-Islam.
During last year's invasion of Iraq, U.S. forces bombed suspected Ansar Al-Islam bases.
Sami Shoresh of RFE/RL's Iraq Service says the U.S. attacks did not put an end to the militant group, however. Members likely found shelter in the so-called Sunni Triangle north of Baghdad, or in the capital itself.
Shoresh says he has little doubt that the group is fighting against U.S. troops in Tikrit, Al-Fallujah, and Mosul. He also believes Ansar Al-Islam is likely to have connections to Al-Qaeda, as well as support from Iran.
Al-Rubay'i insists Ansar Al-Islam is part of a wider terrorist network. "I believe it's part of a terrorist network, the worldwide terrorist network," he said. "There is evidence. As I said, [the evidence] is substantial, but [it] is circumstantial evidence."
Human Rights Watch says, "the existence of any ongoing links between Al-Qaeda and Ansar Al-Islam is unknown."
Terrorism expert Wilkinson says some members of the group may have contact with Al-Qaeda, but he says he's not convinced that Ansar Al-Islam is part of any vast network.
"I know that it has been alleged that it has been penetrated by Al-Qaeda, and in some claims it is claimed that they are totally controlled by them. It is very hard to substantiate that. I have looked through the literature and all the open sources. Obviously, we are an academic institution so we don't have access to classified sources. But in the open source material, it's very difficult to find anything that would conclusively show that they are an agent of Al-Qaeda," Wilkinson said.
Wilkinson says there is no doubt the group survived the attacks by U.S. forces. He says Ansar Al-Islam was able to take advantage of the chaotic situation in Iraq and has survived in these new circumstances.
But he says there is no evidence that the group was able to join the factional fighting in Iraq and that its members have been fighting along with the Sunni Arab-led resistance. Wilkinson says the group "may have its own agenda."