North Korea again denied its involvement in a cyber attack on Sony Pictures on Saturday and offered to jointly conduct an investigation into the case with the U.S. government, as websites of its major propaganda organs continued to remain unstable.

The Federal Bureau of Investigation last week said North Korea was responsible for the Sony hacking, without revealing evidence because of the "protection of sensitive sources." U.S. President Barack Obama said the U.S. would respond "proportionally" to the attack.

"Once again, we make it clear that North Korea has nothing to do with the hacking attacks against Sony Pictures," a spokesperson for the North's powerful National Defense Commission said in a statement carried by the North's official Korean Central News Agency.

"If the U.S. wants to continue to blame us, it must provide evidence right now. If not... the U.S. could jointly conduct an investigation with us behind closed doors."

The communist state has repeatedly balked at Sony's comedy movie "The Interview," which depicts the assassination of its leader Kim Jong-un.

North Korea's Internet went down on Tuesday after an apparent attack amid the cyber security row with the U.S. Access to major North Korean websites remained patchy Saturday for the fifth straight day.

The North also launched a personal attack against Obama, accusing him of instigating the release of the film on Christmas Day and calling him "a monkey living in the rain forest."

"What if somebody made a movie about terror attacks or encouraging the assassination of Obama? Will he welcome the freedom of expression?" the spokesman said.

After the FBI pointed the finger at Pyongyang, Obama said Sony Pictures made a "mistake" in canceling the release of the movie after the cyber attack blamed on North Korea. (Yonhap)