"I absolutely believe that it has to be made very clear we will not allow North Korea to have a deliverable nuclear weapon, and we will approach this from a number of perspectives," Clinton said.
President Barack Obama had earlier said that the US will never accept Pyongyang as a "nuclear state".
Responding to a question, Clinton said she has had conversations in the past with the Chinese about North Korea.
"Up until relatively recently, I think they were under the impression that they could control their neighbour, and they didn't want to crack down because they saw it as a useful card to play. He gets a little crazy, maybe the South Koreans will, you know, move toward them a little bit. He gets a little crazier, maybe they can make some deals with the Japanese about some things they want," she said.
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"Our message to the North Koreans and everyone else listening, they will not be permitted to acquire a nuclear weapon that has a deliverable capacity on a ballistic missile. And we have got to start intensifying our discussions with the Chinese, because they can't possibly want this big problem on their doorstep," she said.
"The regime lives off of luxury goods and the kind of benefits that they then can use to, you know, reward their loyal followers. We have never been able to fully cut that off. So we will do more on sanctions, because that's part of an overall strategy, but that's not enough," she said.
North Korea fired three ballistic missiles off its east coast on September 5. North Korea has conducted a series of missile tests this year. This is the fourth nuclear test since January.
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