Story highlights U.S. secretary of state says Iranian actions against ISIS could have a positive effect

An Iranian military leader says the United States is at a "strategic dead-end"

Regional reports say that Iran bombed ISIS targets in eastern Iraq

Both the U.S. and Iran say their militaries do not communicate

The United States and Iran may be bombing a common enemy in Iraq, one whom they both despise -- ISIS.

Recent media reports from the region claim Iran's military conducted air raids in eastern Iraq, and on Tuesday, a spokesman for the Pentagon said the reports might be true.

"We have indications that they (Iranians) have flown these missions in recent days, these airstrikes in eastern Iraq," Rear Admiral John Kirby told CNN's Wolf Blitzer.

No coordination, U.S. says

Is Iran coordinating with the U.S.-led coalition fighting the Sunni Islamist extremists?

Adamantly, no, came the answer from both sides.

The U.S. is not working with Iran's military, and it is not even directly communicating with it over operations in the country, Kirby said.

JUST WATCHED Iran nuclear talks extended after stall Replay More Videos ... MUST WATCH Iran nuclear talks extended after stall 01:23

JUST WATCHED Iranians still upbeat after failed talks Replay More Videos ... MUST WATCH Iranians still upbeat after failed talks 02:24

"We are not coordinating with nor are we deconflicting with Iranian military," he said. Both sides are leaving it to Iraq to manage their movements in Iraqi airspace and keep them both out of each other's hair.

Speaking from Brussels, Belgium, U.S. Secretary of State John Kerry didn't confirm or deny Iran's military action, saying that's up to the Iraqi or Iranian government. But he did say that while the United States is coordinating its military action with Iraqi authorities, "nothing has changed" as far as its lack of coordination with Iran.

"I think it's self-evident that if Iran is taking (action against ISIS) in some particular place, and it's confined to taking on (ISIS) and it has an impact, it's going to be a net effect that is positive," Kerry said. "But it's not something we're coordinating."

Iran blames U.S. for regional unrest

A high-ranking Iranian military official also vehemently rejected the notion that there may have been any coordinated bombing, and he attacked the United States in his comments.

"The Islamic Republic of Iran blames the United States as the root cause of unrests and problems as well as the terrorist actions of ISIL in Iraq," Gen. Massoud Jazayeri told the government-approved FARS News Agency, adding that Iran wants U.S. influence to completely evaporate.

In another FARS report, the head of Iran's Revolutionary Guard characterized the United States as an enemy, not an ally.

"Today, the Americans are in a strategic dead-end and have experienced all possible options and strategies against the Islamic Revolution, but couldn't attain their desired goals," Maj. Gen. Mohammad Ali Jafari said. "The U.S. capabilities can no more be expanded and their capacities for initiating a change have reached the level of saturation, meaning that the U.S. is left with no more option but admitting the Islamic Republic of Iran's real power."

A common enemy

Yet ISIS is one of few issues that Iran and the United States agree on; both countries want to quash the terror group that has been taking over large swaths of Iraq and Syria.

But with no diplomatic relations with Iran and lingering concerns about its nuclear program , the United States has had to walk a tightrope over Iran's involvement.

This was reflected in comments that U.S. President Barack Obama made to CBS' "Face the Nation."

"There is some deconflicting, in the sense that since they have some troops or militias they control in and around Baghdad ... we let them know, 'Don't mess with us. We're not here to mess with you.' We're focused on our common enemy," Obama said.

Iranians defend Baghdad?

Word of Iranian participation in the fight against ISIS is nothing new.

A military official in Iran has said the world can thank his country that ISIS has not been able to assault Baghdad.

"The (ISIS) terrorists sought to surround Baghdad, but they failed in reaching their ominous goals thanks to Iran's supports," Brig. Gen. Esmayeel Qa'ani told FARS.

Qa'ani is lieutenant commander of the Quds Force, an elite unit of Iran's Revolutionary Guard Corps.

According to FARS, senior military officials in Baghdad said the Quds Force helped free the Iraqi town of Jurf al-Sakher from ISIS control.

Conflicting interests

But the common interest is complicated by diverging interests.

The United States wants to put an end to all Islamist extremism, and in the past, it has accused Tehran of sponsoring terrorism.

Iran itself is an Islamic republic, governed by stringent Islamic law. But the state religion is Shia Islam, which Sunni Muslim extremists, such as ISIS, consider heresy.

Fear of religious tensions

In neighboring Iraq, there is a tense and at times violent schism between Shia and Sunni factions, with the former dominating in government.

Iran has close ties to the Shia faction.

That has stirred fears in Washington that Iran's involvement could not only weaken ISIS, but could also drive the wedge between Iraqis deeper.

"We want nothing to be done that further inflames sectarian tensions in the country," Kirby said of Iranian military actions.

Iran is also a close ally of Syrian dictator Bashar al-Assad , who is battling ISIS as well. Beating back ISIS would take some pressure off of his troops.

The United States is calling for al-Assad's removal.