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12 January 2015 Last updated at 22:04 GMT
The accounts were hacked by a group claiming to support Islamic State, while President Obama was giving a speech on cybersecurity.
Mr Earnest said that officials were monitoring the hack, but cautioned "there is a pretty significant difference between what is a large data breach and the hacking of a Twitter account".
The accounts, which usually provide updates on strikes against IS, have now been suspended.
White House Press Secretary Josh Earnest has played down the significance of a hack involving the Twitter and YouTube accounts of US military command.