Hillary Clinton said the US was considering the position of North Korea
The US is considering reinstating North Korea on its list of states viewed as sponsors of terrorism, Secretary of State Hillary Clinton has said.
North Korea was removed from the list in October 2008 after it began disabling a nuclear reactor, but has since carried out a nuclear test.
Mrs Clinton told ABC News the reason for being removed from the list "is being thwarted by their actions".
Meanwhile, one son of Kim Jong-il says his brother may be named as successor.
Kim Jong-nam, the North Korean leader's eldest son, was asked by Japanese broadcaster NTV whether his younger brother Kim Jong-un would succeed his father.
"I think so. I hear this news by media," he said in reply.
In the interview, which NTV said was conducted in Macau, Kim Jong-nam, 37, said in English: "The appointment of a successor is totally my father's decision."
North Korea raised regional tension last month by declaring it had conducted a nuclear test, firing short-range missiles and issuing threats to its neighbour, South Korea.
Some US senators called for President Barack Obama to reinstate North Korea on the terror list.
Speaking on Sunday, Mrs Clinton said of that suggestion: "Well, we're going to look at it. There's a process for it.
"Obviously we would want to see recent evidence of their support for international terrorism."
She said she could not yet comment on any evidence yet, adding: "Obviously they were taken off of the list for a purpose and that purpose is being thwarted by their actions."
When the US removed North Korea from the terror list, Pyongyang had agreed to allow nuclear experts to take samples and conduct forensic tests at all its declared nuclear facilities and undeclared sites, on mutual consent.
The North was also to allow inspectors to verify that it has told the truth about transfers of nuclear technology and an alleged uranium programme - which North Korea has always denied.
The nuclear test prompted the United Nations to discuss tightening sanctions first imposed in 2006, after the North's first nuclear test.
"We think we're going to come out of this with a very strong resolution with teeth that will have consequences for the North Korean regime," Mrs Clinton said.
"If we do not take significant and effective action against the North Koreans now, we'll spark an arms race in North-East Asia.
"I don't think anybody wants to see that."
Meanwhile, Kim Jong-il's eldest son appears to have confirmed reports his younger brother has been designated the country's next leader.