Pyongyang specifically threatened the White House and the Pentagon in a long statement from the powerful National Defense Commission late on Sunday, Al Jazeera reported.
Such North Korean rhetoric during times of high tension with Washington is routine. But it also underscores the country's sensitivity over a movie whose plot focuses on the assassination of leader Kim Jong-un.
The US blames North Korea for the cyberattack that escalated to threats of terror attacks against US movie theaters and caused Sony to cancel "The Interview's" release.
The United States is now considering whether to put North Korea back on its list of state sponsors of terror, Obama said on Sunday.
"We're going to review those through a process that's already in place," the president said in an interview aired on Sunday on CNN's "State of the Union".
"And we don't make those judgments just based on the news of the day. We look systematically at what's been done and based on those facts, we'll make those determinations in the future."
North Korea had earlier denied responsibility for the hack attack and proposed a joint investigation with the US to to find the culprits.
Obama's remarks, in the interview which was taped on Friday, followed a call from a leading US senator to re-consider North Korea's terror designation.