But according to Major-General Kevin Bergner, a military spokesman, US forces are not participating in the clashes beyond playing a "liaison" role.
Another military spokesman said: "Initial reports indicate that four special group criminals were killed in the air strike."
The US uses the term "special groups" when referring to al-Sadr's Mahdi Army militia.
Armed fighters loyal to al-Sadr have been battling Iraqi troops in the southern city of Basra and in Baghdad for the past two days. The clashes have killed at least 50 people.
The latest fighting broke out in Sadr City, a large poor area in the capital, early on Wednesday. At least 16 mortars were reportedly fired into the Green Zone, home to the US embassy, on Wednesday night causing casualties.
The violence comes after Iraq's security forces launched raids on strongholds of Mahdi Army fighters on Tuesday.
As the fighting broke out, al-Sadr issued a statement calling for demonstrations across the country and threatened "civil disobedience" if attacks by US and Iraqi forces on members of his movement continued.
"We demand that religious and political leaders intervene to stop the attacks on poor people," a statement read by Hazam al-Aaraji, an al-Sadr representative, said.Looming deadline
"We call on all Iraqis to launch protests across all the provinces. If the government does not respect these demands, the second step will be general civil disobedience in Baghdad and the Iraqi provinces."
|Al-Sadr has called for 'civil disobedience'|
Nuri al-Maliki, Iraq's prime minister, imposed a deadline for those fighting security forces in Basra to surrender.
"Those who were deceived into carry weapons must deliver themselves and make a written pledge to promise they will not repeat such action within 72 hours," he said on Wednesday.
"Otherwise, they will face the most severe penalties."
Al Jazeera's James Bays, reporting from Baghdad, said that a spokesman for al-Maliki said that some fighters had surrendered.
He said: "But we are getting reports that heavy fighting is continuing in parts of Basra."
"I think the prime minister is trying to put his stamp in this operation. No one expected that he would go to Basra."
"Al-Maliki wants to show that he is in control, because in the past, he was seen as a weak, impotent leader."
The US claims that members of the so-called "special groups" are trained in Iran in the use of sophisticated weaponry, including rockets and lethal roadside bombs known as "explosively formed penetrators" that can cut through US armoured vehicles.
Amid the accusations, the military says that Iran could contribute to ending the violence in Iraq, calling on Tehran to use its influence to assist in improving security in Basra.
Bergner said: "There is no question that the government of Iran has significant influence in Basra, in the province and in southeastern Iraq in general.
"We would love to see the government of Iran fulfil its commitments to help improve security and stability [in Basra] ... and reduce the activities of those operating outside the law."
Bergner also said the operation was aimed at improving security in the Basra province ahead of provincial elections in October.
"The prime minister's assessement is that without this operation there will not be any hopeful prospect of improving security in Basra," Bergner said.
Falah Shenshal, a member of parliament allied to al-Sadr, told Al Jazeera that al-Maliki was targeting political opponents.
"They say they target outlaw gangs, but why do they start with the areas where the sons of the Sadr movement are located?"
"This is a political battle ... for the political interests of one party [al-Maliki's Dawa party] because the local elections are coming soon.
"They are using the law for their political interests. We will ask the parliament to drop confidence from the Maliki government."
The Mahdi Army has grown frustrated with a ceasefire imposed by al-Sadr last year.
Its fighters say the ceasefire has been abused by US and Iraqi forces to make indiscriminate arrests ahead of provincial elections.
The US military says it is targeting only "rogue" members who have broken the ceasefire, and has cited the truce as a main factor in a significant drop in violence across the country.