BAGHDAD, Iraq (CNN) -- A Shiite Muslim militia involved in the warfare between Sunni and Shiites in Iraq has received "millions of dollars" and an assortment of weaponry from Iran, a senior U.S. military official says.

The official said Iran -- which is overwhelmingly Shiite and largely Persian -- tries to spread its largess to other militants as well, but can wield only so much influence throughout Iraq -- which, while predominantly Shiite, is largely Arab.

He said Iran is not trying to fuel cινιℓ ωαr in Iraq, but rather is trying to make sure it retains some influence with whichever group comes out on top in Iraq.

The official, who asked to remain anonymous, briefed reporters Wednesday about the conflict in Iraq. A transcript of that briefing was issued Thursday. (Watch why the U.S. strategy may fail in Iraq -- 1:45)

A good deal of the briefing involved the Mehdi Army, or Jaish al-Mahdi, the militia of the powerful Shiite cleric Muqtada al-Sadr.

The group, which has power bases in the Shiite south and in Baghdad's Sadr City, has gained in political influence in the past year, with visible presence in the Iraqi government.

Asked how much money Iran has given the Mehdi Army this year, the official said, "I don't have a good estimate, but I'll tell you, it's in the millions of dollars."

The official said that high-grade military explosives and specialized timers are among the "boutique military equipment" moving from Iran into Iraq.

Some of the equipment is of the same type that Hezbollah, an Iranian-backed Shiite militia, used against Israeli forces in Lebanon during the summer, the official said.

The origin of the weapons was easy to discern because of Iranian markings on it, he said. Because Iran maintains tight control over armaments, he said, shipment of the weapons into Iraq had to involve "elements associated with the Iranian government."

The official said Iran wants "control of surrogates" in Iraq, not an easy task because Iraqi Arab nationalist groups, not pro-Iranian groups, have more grass-roots support.

Iran has "only has a window of opportunity" before historic animosities between Arab Iraq and Persian Iran prevail, he said.