Pyongyang specifically threatened the White House and the Pentagon in a long statement from the powerful National Defence Commission late on Sunday.
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 cyber attack that escalated to threats of terror attacks against US movie theatres and caused Sony to cancel the release of "The Interview".
The US 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 judgements 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."
'A dangerous precedent'
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 reconsider North Korea's terror designation.
Robert Menendez, chairman of the Senate Foreign Relations Committee, wrote to Secretary of State John Kerry on Friday, saying the Pyongyang regime had set a "dangerous precedent" through cyber attacks that were "able to inflict significant economic damage on a major international company".
The State Department rescinded its designation of North Korea as a state sponsor of terrorism in October 2008. Currently, the list includes just four countries: Cuba, Iran, Sudan and Syria.
Obama has asked the State Department to consider removing Cuba, following the historic thawing of relations between the two Cold War rivals announced earlier this week.