WASHINGTON, Dec 15 (Reuters) - Russian hackers seized control last year of the unclassified email system used by the U.S. military's Joint Chiefs of Staff, CBS News reported on Thursday, citing an interview with then-Joint Chiefs of Staff Chairman Martin Dempsey.

Dempsey, who did not appear on camera, said he was alerted to the August 2015 attack by an early morning phone call from the director of the National Security Agency, Admiral Mike Rogers, according to CBS.

The email system is used by the Pentagon's Joint Staff, an organization of some 3,500 military officers and civilians who work for the chairman.

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The hackers seized the passwords and electronic signatures used by Dempsey, an Army general who retired in September 2015, and hundreds of other senior officers to sign on to the network, according to CBS. The only way to stop the attack was to take the network down, CBS said.

The attack, which U.S. officials now blame on Russia, was not spying, but a full-on assault whose only apparent purpose was to cause damage and force the Pentagon to replace both hardware and software, which took about two weeks to accomplish, according to CBS.

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The motive for the attack was believed to be Russian anger at economic sanctions orchestrated by the Obama administration in response to Russian President Vladimir Putin's annexation of Crimea and interference in Ukraine, CBS said.

The Pentagon declined to comment.

U.S. officials have accused Putin of supervising his intelligence agencies' hacking of the U.S. presidential election in an effort to help Republican Donald Trump. Russian officials have denied accusations of interference in the Nov. 8 election won by Trump.

(Writing by Eric Beech; Editing by Peter Cooney)