As North Korea vowed to retaliate "thousands-fold" against the new U.N. economic sanctions sponsored by the U.S., Secretary of State Rex Tillerson offered to negotiate if the North stops testing missiles and halts its nuclear weapons program. The sanctions were unanimously approved by the U.N. Security Council, including Russia and China.

However, according to Nicholas Burns, a former U.S. ambassador to NATO and undersecretary of state for political affairs during the George W. Bush administration, it is "unlikely" the sanctions will "ultimately work."

"This was a victory for the Trump administration, to see these sanctions, to convince China and Russia to join. But the North Koreans prize above all else the possession of these nuclear weapons," Burns said Monday on "CBS This Morning."

China, which "has the most leverage," doesn't want to see the North Korean regime collapse, said Burns, who is now a professor at Harvard's Kennedy School.

"They don't want to see refugees go into China. They don't want to see the Korean peninsula unified by the South Korean government aligned with the United States because that would be a victory strategically for this long-running competition between China and the United States and Asia," Burns said.

Burns contrasted the North Korean sanctions and the sanctions imposed on Iran by the U.S.

"You remember a couple of years ago these tremendous financial and economic, oil and gas sanctions on Iran. Iran's a trading nation. They wanted to be connected economically to the rest of the world, so those sanctions worked to drive them to the negotiating table," Burns said. "North Korea is a hermit kingdom. They're isolated. They don't trade with many countries. And I think Kim Jong Un, this young leader of North Korea, believes that his possession of nuclear weapons is his ultimate protection against any foe, most especially the United States."

North Korean Foreign Minister Ri Yong Ho said Monday that "under no circumstances" will it put its nuclear weapons or ballistic missiles on the negotiating table. He made that statement at a conference of the Association of Southeast Asian Nations (ASEAN) in Manila, Philippines.

Bringing North Korea to the negotiating table for an interim arrangement might be "a messy compromise," Burns said, "but it'd be a lot better than the current situation."

"They're not constrained right now, and they are racing towards a nuclear weapon, and that's a real threat to our country," Burns said.