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BAGHDAD - Iranian intelligence operatives have been training Iraqi fighters inside Iran on how to use and assemble deadly roadside bombs known as EFPs, the U.S. military spokesman said Wednesday.

Commanders of a splinter group inside the Shiite Mahdi Army militia have told The Associated Press that there are as many as 4,000 members of their organization that were trained in Iran and that they have stockpiles of EFPs, a weapon that causes great uneasiness among U.S. forces here because they penetrate heavily armored vehicles.

U.S. military spokesman Maj. Gen. William Caldwell would not say how many militia fighters had been trained in Iran but said that questioning of fighters captured as recently as this month confirmed many had been in Iranian training camps.

"We know that they are being in fact manufactured and smuggled into this country, and we know that training does go on in Iran for people to learn how to assemble them and how to employ them. We know that training has gone on as recently as this past month from detainees debriefs," Caldwell said at a weekly briefing.

EFP stands for explosively formed penetrator, deadly roadside bombs that hurl a fist-size lump of molten copper capable of piercing armor.

In January, U.S. officials said at least 170 U.S. soldiers had been killed by EFPs.

Caldwell also said the U.S. military had evidence that Iranian intelligence agents were active in Iraq in funding, training and arming Shiite militia fighters.

"We also know that training still is being conducted in Iran for insurgent elements from Iraq. We know that as recent as last week from debriefing personnel," he said.

"The do receive training on how to assemble and employ EFPs," Caldwell said, adding that fighters also were trained in how to carry out complex attacks that used explosives followed by assaults with rocket-propelled grenades and small arms.

"There has been training on specialized weapons that are used here in Iraq. And then we do know they receive also training on general tactics in terms of how to take and employ and work what we call a more complex kind of attack where we see multiple types of engagements being used from an explosion to small arms fire to being done in multiple places," he said.

The general would not say specifically which arm of the Iranian government was doing the training but called the trainers "surrogates" of Iran's intelligence agency.

Caldwell opened the briefing by showing photographs of what he said were Iranian-made mortar rounds, RPG rounds and rockets that were found in Iraq.

The U.S. military also announced two more soldier deaths: One soldier was killed and two were wounded by a roadside bomb Wednesday in an eastern section of the capital, and another soldier died a day earlier in an attack in southern Baghdad. One soldier was wounded in that incident.

At least 3,287 members of the U.S. military have died since the beginning of the war in 2003, according to an AP count. The figure includes seven military civilians.

Also Wednesday, Iraqi Cabinet ministers allied to radical cleric Muqtada al-Sadr threatened to quit the government to protest the prime minister's lack of support for a timetable for U.S. withdrawal.

Such a pullout by the very bloc that put Prime Minister Nouri al-Maliki in office could collapse his already perilously weak government. The threat comes two months into a U.S. effort to pacify Baghdad in order to give al-Maliki's government room to function.

Meanwhile, bodies lay scattered across two central Baghdad neighborhoods after a raging battle left 20 suspected insurgents and four Iraqi soldiers dead, and 16 U.S. soldiers wounded, witnesses and officials said.

The fighting Tuesday in Fadhil and Sheik Omar, two Sunni enclaves, was the most intense since a massive push to pacify the capital began two months ago.

Al-Sadr's political committee issued a statement a day after al-Maliki rejected an immediate U.S. troop withdrawal.

"We see no need for a withdrawal timetable. We are working as fast as we can," al-Maliki said on his four-day trip to Japan, where he signed loan agreements for redevelopment projects in Iraq.

"To demand the departure of the troops is a democratic right and a right we respect. What governs the departure at the end of the day is how confident we are in the handover process," he said, adding that "achievements on the ground" would dictate how long American troops remain.

Al-Maliki spoke a day after tens of thousands of Iraqis took to the streets of two Shiite holy cities, on al-Sadr's orders, to protest the U.S. presence in their country. The rally marked the fourth anniversary of the fall of Baghdad at the hands of American forces.

"The Sadrist movement strongly rejects the statements of Prime Minister Nouri al-Maliki, in which he stood by the continued presence of occupation forces despite the will of the Iraqi people," said the statement, a copy of which was obtained by the AP. "The Sadrist movement is studying the option of withdrawing from the Iraqi government -- a government that has not fulfilled its promises to the people," it said.

"We are serious about withdrawing," it added.

It would not be the first time the Sadrists, who hold six seats in the Cabinet, left al-Maliki's government.

Al-Sadr's ministers and 30 legislators boycotted the government and parliament for nearly two months to protest a November meeting between al-Maliki and President Bush in Jordan.

The statement expressed anger over the Baghdad security plan launched Feb. 14, calling it "unfair." Iraqi and U.S. troops have been targeting members of al-Sadr's Mahdi Army militia, which has been blamed for sectarian killings.

Later in the day, the head of al-Sadr's bloc in parliament, Nassar al-Rubaie, said U.S. troops had taken over al-Sadr's office in the city of Diwaniyah, the scene of weekend clashes between U.S. and Iraqi troops and al-Sadr's militiamen.

"We say that this matter is very dangerous and we put the blame on the Iraqi government for the American destruction of the country," he said. "We have thought before that sovereignty in Iraq is incomplete, but now we say that sovereignty doesn't exist in Iraq," al-Rubaie said.

Caldwell said he has no information about the alleged takeover of the office.

Iraqi soldiers held a security cordon around Fadhil, and residents hid frightened in their homes, a witness told the AP by telephone, on condition of anonymity out of fear for his safety.

The Muslim Scholars Association, a Sunni group, issued a statement quoting witnesses as saying Tuesday's battle began after Iraqi troops entered a mosque and executed two young men in front of other worshippers. Ground forces used tear gas on civilians, it said.

"The association condemns this horrible crime carried out by occupiers and the government," the statement said.

But the witness in Fadhil said the two men were executed in an outdoor vegetable market, not in the mosque. The Iraqi military was not immediately available to comment on the claim.

The U.S. military said the battle began after American and Iraqi troops came under fire around 7 a.m. during a routine search operation. Helicopter gunships then swooped in, engaging insurgents with machine gun fire, the military said.

Some Arab TV stations reported a U.S. helicopter was shot down in the fight, and showed video of a charred piece of mechanical wreckage that was impossible to identify. Caldwell said four helicopters sustained minor damage but were able to return to base. He confirmed that one Apache gunship had dropped a missile pod as it left the area.

Caldwell said 13 of the 16 wounded Americans had returned to duty and that 20 suspected insurgents were killed and 30 wounded, he said.