Three political parties -- the Kurdish Democratic Party, or KDP; the Patriotic Union of Kurdistan, or PUK; and the Supreme Council for the Islamic Revolution in Iraq, or SCIRI -- possess the strongest militias in the country.
Other political parties also have their own armed militias, but retain much smaller numbers of men.
David Hartwell, Middle East editor at the British-based "Jane's Sentinel Security Assessments," says the KDP has thousands of seasoned and well-armed fighters.
"The KDP, who are the Kurdish Democratic Party, have got 15,000 guerrillas with another 25,000 tribal militia," says Hartwell.
The PUK, the party of President Talabani, has some 15,000 guerrillas and some 20,000 tribal militia fighters.
Before the fall of Saddam Hussein, Kurdish forces fought the Iraqi Army for several years, while PUK and KDP militias also fought a war against each other.
Hartwell says that the Kurdish fighters, or Peshmergas, are not badly armed for a militia, but are not on the same level as a regular army.
"I think the heaviest thing that they've got probably is heavy artillery. You know, rocket launchers. I don't think there's anything particularly sophisticated about the weaponry they've got," Hartwell says.
The analyst says Kurds bought heavy weaponry on the black market abroad and also in Iraq itself. Many of the fighters received training when they were army conscripts in the Iraqi Army. Others were likely trained by U.S. Special Forces before the war.
Another prominent militia, the Shi'ite Badr Brigade is an armed wing of SCIRI.
The exact number of fighters in the brigade is not known, but there are estimates of several thousand. The force consists mainly of men who fled to Iran under Saddam Hussein's rule.
Alireza Nourizadeh, director of the Center for Arab and Iranian Studies in London, says the Badr Brigade is a serious fighting force. However, he adds that the group's close ties with Iran cast some doubts about its loyalties.
"I'm sure among them, at least a couple of thousand are real fighters and they will be very good fighters, but the problem is about their loyalty. First of all, many of them never saw Iraq before the collapse of the Iraqi regime, the toppling of the Saddam regime. Some of them were born in Iran and they were educated in Iran. Their Persian is much better than their Arabic. And their loyalty is to Ayatollah Khomeini, to the Iranian government, to Iranian security, not to the Iraqi [state]," says Nourizadeh.
Hartwell also speculates that the Badr Brigade has likely received training along the same lines as the militant group Hizbullah, although its weaponry is unsophisticated.
In the recent BBC interview, President Talabani regretted that the United States was opposed to using militia forces. He argued that "we have inner forces [able] to eradicate the terrorists," and that they should be brought into the fight.
However, analysts say they cannot imagine these Kurdish and Shi'ite fighters coming to Sunni areas to introduce law and order.
Hartwell says this move would only make the security situation worse and could bring the country to the brink of a sectarian war.
"In the wider picture, it doesn't really work when you knit it all together with the Shi'a and the Sunnis and how that is perceived, I can't imagine the Americans are in the mood for this [militias suppressing the insurgency]," Hartwell says.
Nourizadeh agrees that militias will only gravely exacerbate the situation in Iraq.
However, he says the new Iraqi government should do everything it can to integrate both Kurdish fighters and the Badr Brigade into the national army. This, he says, would not only elevate their status, but it would also increase the fighting capabilities of regular troops.