Kim Jong Un's constant concern about being overthrown as leader of North Korea complicates any dealings with the reclusive nation over its nuclear missile program, said Bill Richardson, whose past diplomatic missions included negotiations with Pyongyang.

Richardson, formerly ambassador to the U.N. and Energy secretary during Bill Clinton's presidency, said on CNBC's "Squawk on the Street" Wednesday that President Donald Trump's "fire and fury" threat against North Korea was "over the top."

"You never know how the North Koreans are going react ... especially Kim Jong Un who's afraid of his own shadow, who is concerned about him being toppled, regime change," said Richardson, adding he was encouraged that Secretary of State Rex Tillerson tamped down Trump's rhetoric.

Returning from a trip to Asia, Tillerson said early Wednesday: "I think Americans should sleep well at night. I have no concerns about this particular rhetoric of the last few days." Tillerson made the comments on a refueling stop in Guam, the U.S. territory that North Korea threatened to bomb.

State media in North Korea said late Tuesday Pyongyang was considering a strategy to strike Guam.

Hours earlier, Trump warned North Korea about facing "fire and fury" if it continued to make threats against the U.S. after intelligence showed the isolated nation successfully created a miniaturized nuclear weapon designed to fit inside its missiles.

Trump doubled down on the tough talk in tweets Wednesday morning.

My first order as President was to renovate and modernize our nuclear arsenal. It is now far stronger and more powerful than ever before....

...Hopefully we will never have to use this power, but there will never be a time that we are not the most powerful nation in the world!

"This is the gravest situation I've seen in the Korean Peninsula in a very long time," said Richardson, but he insisted "it's not a crisis situation" yet.

Richardson, a Democratic former governor of New Mexico, said the U.S. should aim to get North Korea to agree to pause its weapons tests in exchange for a dialogue "to see if there's common ground."

Meanwhile, the United Nations Security Council unanimously imposed new sanctions on North Korea on Saturday that could cut its $3 billion annual export revenue by a third.

"This is the first sanction on North Korea that has some bite. But it's only going to happen if China stops the cross-border smuggling and they enforce the sanctions," said Richardson, who unsuccessfully ran for the 2008 Democratic presidential nomination.

Richardson currently runs a foundation, the Richardson Center for Global Engagement, which aims to mediate prisoner releases and international conflicts.

Recently, he worked to free American college student Otto Warmbier, who was held for 17 months by North Korea after being convicted of stealing. In June, the 22-year-old was sent home on what Pyongyang said was humanitarian grounds. Warmbier, who was in a coma for a year, died shortly thereafter.

— Reuters and The Associated Press contributed to this report.