“I think it’s self-evident that if Iran is taking on ISIL in some particular place and it’s confined to taking on ISIL and it has an impact … the net effect is positive,” Kerry said, using one of the acronyms for the group. “But that’s not something that we’re coordinating. The Iraqis have the overall responsibility for their own ground and air operations, and what they choose to do is up to them.”

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That’s a noteworthy reaction after decades in which Iran and the United States have been on the opposite of national security issues. From the Iranian hostage crisis that ended in 1981, to the support the U.S. gave Iraqi President Saddam Hussein in a war against Iran in the 1980s, to the ongoing tensions of Iran’s nuclear program, Washington and Tehran have long been at odds with one another.

During the Iraq war, U.S. officials accused Tehran of supplying weapons to Shiite militia groups that attacked American troops. And in Afghanistan, Iran has exerted influence by providing support to Taliban insurgents fighting U.S. and coalition troops, while at the same time cultivating relationships in the Afghan central government, according to a 2011 analysis prepared by the Rand National Defense Research Institute for Marine Corps intelligence officials.

Iran spurned an American request for cooperation against the Islamic State in September, with its supreme leader, Ayatollah Ali Khamenei, calling the coalition formed “empty, shallow & biased” on Twitter. President Obama wrote a letter to Khamenei afterward to tell him Tehran and Washington had shared interests in Iraq, but Iran is believed to exert its military influence there on its own without any American involvement.

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Several Iraqi military victories against the militants this fall have come with Iranian involvement, and the commander of Iran’s Quds force, Gen. Ghasem Soleimani, has paid a visit to Iraq, according to the Associated Press. Lebanon’s Hezbollah militia group — long backed by Iran — also may have been involved.

The Pentagon press secretary, Adm. John Kirby, said Tuesday that he had seen the media reports about Iran launching airstrikes on the Islamic State, and had no reason to doubt them. But he declined to take any position on them.