Susan Rice. Screenshot via CNN

Susan Rice, who served as US national security adviser in the Obama administration, on Thursday said this week's verbal tug-of-war between President Donald Trump and North Korean leader Kim Jong Un was proof that Trump faced a "very real challenge" confronting the unpredictable regime.

"When the president of the United States makes statements that could be mistaken for Kim Jong Un's, I think that rattles our allies enormously and it risks a miscalculation on the North Korean side," Rice told CNN's Wolf Blitzer.

On Tuesday, Trump used much harsher rhetoric than past US leaders had against North Korea, declaring that the country would feel "fire and fury like the world has never seen" if it kept threatening the US. Kim promptly responded with another threat — this time against the US Pacific territory of Guam.

"We need to be very measured, very careful, very planned in our rhetoric," Rice said. "I hope that we will see more measure out of the administration and out of the president as he approaches this very real challenge.”

When asked whether the US could realistically consider a preemptive attack on North Korea, Rice, who also served as the US ambassador to the United Nations, said the outcome would be "catastrophic" for the Korean Peninsula and put the US at risk of a direct confrontation with China, North Korea's closest ally.

"A preemptive attack by the United States would be a very, very poor choice, a very dangerous choice," Rice said, adding a warning for Kim's government: "The North Koreans understand that if ever they were to use their nuclear weapons against the United States or our allies, they would face annihilation."

Despite bipartisan lamentations about the perceived loss of measured diplomacy between the US and North Korea this week, experts have argued that an actual nuclear conflict is unlikely. As Business Insider's Alex Lockie wrote on Wednesday: "Trump didn't call for a strike, and he won't. Neither will Kim Jong Un. Both men will get acceptable outcomes without firing a shot."