The "unceremonious" firing of Secretary of State Rex Tillerson is "very concerning," especially in light of the upcoming summit between President Donald Trump and North Korean leader Kim Jong Un, said Bill Richardson, whose past diplomatic missions included negotiations with Pyongyang.

Last week, Trump accepted an invitation to meet with Kim by May, although it has yet to be arranged The two leaders have exchanged barbs in the past over North Korea's nuclear program.

Richardson told CNBC's "Closing Bell" on Tuesday that the meeting is "the most significant negotiations I think the country is going to have during the first term."

And those negotiations have to be led by a secretary of State, contended Richardson, who formerly served as ambassador to the United Nations and as Energy Secretary under former President Bill Clinton.

Therefore, he believes the meeting should be delayed by a month.

Trump fired Tillerson earlier Tuesday in a tweet and tapped CIA Director Mike Pompeo to fill the position.

However, Pompeo first needs to be confirmed by Congress.

"Pompeo is going to take a least a month to get confirmed. He's got to get up to speed," Richardson said. "He's an intelligence official … but he's got to learn about Asia, diplomacy. He's got to learn about many issues relating to the State Department."

He added, "I just don't understand why there's such a rush to move ahead" on the North Korea meeting. "Do it right. Do it with a full national security team."

A senior administration official told CNBC last week that the development was just a meeting and not a promise of sanctions relief or concessions from the U.S.

"We're not even talking about negotiations," he said. "The president is not prepared to reward North Korea in exchange for talks, but he's willing to meet and he expects North Korea to start putting action to these words."

The White House did not immediately respond to a request for comment on Richardson's remarks.

— CNBC's Amanda Macias and Christina Wilkie contributed to this report.