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KIRAN CHETRY: A propaganda video used to recruit fighters to kill U.S. soldiers. They are being targeted on the tape obtained by CNN. The U.S. military says it is proof Iran is training an elite militia inside of Iraq.

CNN's Michael Ware is breaking this story from Baghdad.

(BEGIN VIDEOTAPE)

MICHAEL WARE, CNN INTERNATIONAL CORRESPONDENT (voice-over): These men are well-trained to kill American soldiers in Iraq. They belong to what U.S. military intelligence calls the Special Group.

This video obtained by CNN shows them firing against U.S. targets. Elite groups of Shiite fighters trained in guerilla warfare by the militant Lebanese group Hezbollah, they are armed and directed by Iran.

GEN. DAVID PETRAEUS, TOP U.S. COMMANDER IN IRAQ: Clearly, again, the Iranian-supported Special Groups are right now again a very, very difficult enemy. They are killing our soldiers. They are shooting rockets at the Iraqi seat of government, at the International Zone.

WARE: U.S. military intelligence says Iranian-backed militia like this are killing more U.S. soldiers each month than al Qaeda or the Sunni insurgency. And the U.S. now rates Iran as an equal or greater threat than al Qaeda in Iraq.

U.S. intelligence says Iranian-made weapons are still flooding across the border -- some seized in April with 2008 markings. It also claims that captured members of the Special Groups have admitted they were trained inside Iran. But it's very hard for the U.S. to prove continuing Iranian involvement with the Special Groups.

It's most recent dossier of evidence sent to Tehran with an Iraqi delegation merely adds fresh detail to old allegations. And on his last visit to Tehran, Iraq's Prime Minister Nuri al-Maliki carried his own dossier of evidence implicating Iran, yet even his senior aides says it's weak.

HAIDAR ABADI, MALIKI ADVISER: I mean, look, you may ask us for evidence, we cannot produce watertight evidence. We cannot. Because the Iranians, they have experience, with even the previous regime, of infiltrating the borders, causing problems for many years. They have that experience without being exposed.

WARE: Iran also had strong ties to the major political parties that make up the governing coalition in Baghdad, with even Iraq's president considered by U.S. intelligence to be an Iranian agent of influence. All of which the U.S. has to accept as a fact of life.

PETRAEUS: Again, it's a reality.

WARE: That there is that kind of infiltration.

PETRAEUS: It's a reality. Again, look, as you pointed out earlier but again for the listeners, your audience, these parties are products, many of them, of time in Iran.

WARE: And though Iran's influences is believed to be growing, Petraeus says he still sees a possible opportunity here with some Iraqi politicians connected to Iran becoming anxious about Iran's Special Groups.

PETRAEUS: You see leaders of parties that again have benefited financially, physically and all kinds of different ways from their relationships with Iran now being gravely concerned about what the Special Groups, and to a degree the militias, are doing in Iraq.

WARE: The Iraqi Army has moved against Shia militia in Sadr City and in the port of Basra, the operations ending after ceasefires -- at least one brokered by Iran -- were declared. So that leaves the Special Groups -- who the U.S. says are responsible for a huge car bombing in Baghdad on Tuesday -- as the tip of Iran's military spear in Iraq.

At last Friday's prayers, anti-American rebel cleric Muqtada al-Sadr announced the creation of a new group in his Mahdi Army militia to fight U.S. troops, meaning Iran's Special Groups may have just found a political sponsor inside Iraq. With the success of America's mission at stake, for General Petraeus this is a critical time.

PETRAEUS: Well, I think again the question is what is the character of that involvement? How malign is it? Do they allow Iraq to succeed again as the first Shia-Arab state. To let this new country in this ancient land actually prosper and flourish or do they somehow try to control it or use it as a tool.

WARE: Yet the Iraqi government said if Iran promises not to interfere in Iraq's affairs, it will forge closer security ties with Tehran.

ABADI: It will open the gate for full cooperation with Iran. There can be security training. We can benefit a lot from Iran. The Iranians have a lot of experience, counter-intelligence, experience of counter-terrorism.

WARE: But while these Special Group attacks continue against U.S. bunkers and American soldiers, an alternative to the rising Iranian influence is precisely what America needs.

Michael Ware, CNN, Baghdad.