Story highlights North Korean leader Kim Jong Un held out a rare olive branch to South Korea

"We won't take any of the talks seriously if they don't do something to ban all nuclear weapons," Haley said

Washington (CNN) US Ambassador to the United Nations Nikki Haley issued a stern warning to North Korea on Tuesday, saying the US "will never accept a nuclear North Korea."

"As we hear reports that North Korea might be preparing for another missile test -- I hope that does not happen, but if it does -- we must bring even more measures to bear on the North Korea regime," she said. "The civilized world must remain united and vigilant against the rogue state's nuclear arsenal. We will never accept a nuclear North Korea."

North Korean leader Kim Jong Un held out a rare olive branch to South Korea on Monday, offering talks about sending a delegation to the Winter Olympics in Pyeongchang next month.

Kim struck an unusually conciliatory note in his annual New Year's Day address, declaring his wish "for peaceful resolution with our southern border."

He also warned the United States that North Korea's nuclear ambitions were now complete and the launch button was "always on the desk in my office."

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