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Iran's Supreme Leader Ayatollah Ali Khamenei waves to members of the paramilitary Basij force at the Imam Khomeini Grand Mosque in Tehran, Iran, Nov. 20, 2013. AP/Office of the Supreme Leader

TEHRAN, Iran - A top security official in Iran said Wednesday the Islamic Republic has written back in response to letters sent by U.S. President Barack Obama, the first acknowledgement of such correspondence. However, it's not clear whether Supreme Leader Ayatollah Ali Khamenei wrote the letters himself.

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The White House confirmed Thursday that President Obama sent a letter to Iran's supreme leader Ayatollah Ali Khamenei about the country's nuclear...

The letter writing is part of a recent thaw in relations between the two countries since the 1979 Islamic Revolution that toppled the U.S.-backed shah and the storming of the U.S. Embassy in Tehran, where 52 Americans were held hostage for more than a year. It also comes as a U.S.-led coalition battles the Islamic State of Iraq and Syria (ISIS) in neighboring Iraq and as Iran and world powers negotiate a permanent deal regarding the country's contested nuclear program.

"This is not the first time that such a thing has taken place," said Ali Shamkhani, the secretary of Iran's Supreme National Security Council, during an appearance on state television Wednesday night. "It had previously taken place and necessary response was given to some of them."

According to the Wall Street Journal, Obama's recent letter to Khamenei described a shared interest between the U.S. and Iran in fighting ISIS and stressed that any cooperation on that would be largely contingent on Iran agreeing to the nuclear deal.

However, CBS News senior White House correspondent Major Garrett reports those familiar with the Obama-Khamenei correspondence say public denials reinforce the perception within Khamenei's inner circle that he has a secret back-channel to Obama. U.S. officials would not disclose the contents of Obama's letter, but disputed the Journal's contention the letter sought to link still-nettlesome nuclear negotiations with Iran's support to fight the ISIS in Iraq.

White House officials emphasized Thursday that Obama's negotiators have kept nuclear talks separate from any U.S. conversations with Iran about battling ISIS (which the White House calls ISIL) in Iraq.

Shamkhani said Iran responded "that we can't accept at all to have a decorative, caricaturistic nuclear industry."

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Are Iran's Ayatollah and Obama pen pals now?