'We want to step back from the brink' on North Korea: Former ambassador

Sanctions against North Korea should be the "first resort," with the military option on the table, former ambassador Nancy Soderberg told CNBC on Tuesday.

In fact, Nikki Haley, U.S. ambassador to the United Nations, has scored "one of the most impressive diplomatic victories" in the U.N. Security Council, said Soderberg, who served as ambassador to the U.N. and deputy national security advisor under President Bill Clinton .

In August, the council unanimously imposed new sanctions on Pyongyang that could slash its $3 billion annual export revenue by a third.

"Let the sanctions bite, see if you can really make the North Koreans feel the squeeze and start trying to deny the funds that enable him to build these weapons," Soderberg said, referring to North Korean leader Kim Jong Un .

"We want to step back from the brink."

On Sunday, North Korea said it successfully carried out a test of a hydrogen bomb intended to be carried by an intercontinental ballistic missile. Trump then tweeted that the U.S. is considering stopping all trade with any country doing business with North Korea.

"We need to look at some financial sanctions, trade sanctions, things like that. We're clearly not going to cut off all of our trade with China," she said, calling that threat "unrealistic."

Tensions between the U.S. and North Korea have been escalating. Last month, after a previous provocation from North Korea, President Donald Trump said Pyongyang's threats would be met with " fire and fury ."

Soderberg told " Power Lunch " she doesn't think those types of threats are helpful.

"I don't think it was wise for the president to extemporaneously threaten nuclear war with North Korea. That's just ramping up the tensions on all sides and dividing a wedge with our allies in South Korea and Japan," she said.

On Monday, Haley told the U.N. Security Council that Kim Jong Un was "begging for war" and urged the council to impose the "strongest possible" sanctions to deter him and shut down his trading partners.

— CNBC's Leslie Shaffer and Reuters contributed to this report.