The US-based internet monitoring company Dyn said the reason for the outage was not known but could range from technological glitches to a hacking attack.
Dyn said it was difficult to say how much of North Korea’s internet had been restored.
The website for the state-run Korean Central News Agency (KCNA) and Rodong Sinmun newspaper were back online on Tuesday, but other websites were inaccessible.
Several US officials close to the investigations of the attack on Sony Pictures said the US government was not involved in any cyber action against Pyongyang.
US President Barack Obama vowed on Friday to respond “proportionally” to the major cyber-attack, which he blamed on North Korea, “in a place and time and manner that we choose.”
Despite being blamed for the cyber-attack on Sony Pictures, North Korea has barely 1,000 internet addresses and the public can only access one intranet service.
Meanwhile South Korea, which remains technically at war with the North, said it could not rule out the involvement of its isolated neighbour in a cyber-attack on its nuclear power plant operator. It said only non-critical data was stolen and operations were not at risk, but had asked for US help in investigating.
On Monday North Korea threatened the United States, calling it a “cesspool of terrorism” and accusing the Obama administration of being behind the film The Interview.
In a statement released via the state news agency KCNA, North Korea said its “toughest counteraction will be boldly taken against the White House, the Pentagon and the whole US mainland”.