As the Trump administration prepares for a summit between President Trump and North Korean leader Kim Jong Un, former Secretary of State Condoleezza Rice advised caution: "I have no problem with negotiating with them. But beware."

Rice, who negotiated with the North while she was serving in President George W. Bush's administration, had what she called three "admonitions" for the administration:

"Don't forget that there are other interested parties. For instance, Japan has a very important interest here. Secondly, take it one step at a time. It's fine to talk about a peace treaty on the Korean Peninsula. In fact, we talked about a peace treaty. That should be the ultimate goal. But go step by step, make sure there's good verification of everything the North Koreans are doing, and keep your eye on the prize of denuclearization. Because what we want to do is stop them short of threatening the American homeland," Rice said. "And finally, remember the nature of this regime. This is a regime that murdered an American citizen just a year ago, this is a regime where the leader killed his half-brother in Malaysia... It's a brutal regime, a secretive regime."

South and North Korea's historic agreement last week for a "new era of peace" and denuclearization in the Korean Peninsula set the stage for Mr. Trump's meeting with Kim, which will likely happen in the next three or four weeks. The final two summit locations under consideration are Singapore and Mongolia, administration sources told CBS News chief White House correspondent Major Garrett.

Rice, who co-authored a new book called "Political Risk: How Businesses and Organizations Can Anticipate Global Insecurity" with fellow Stanford professor Amy Zegart, gave former Secretary of State Rex Tillerson credit for getting North Korea to the table.

"[The North Koreans] have a tendency when they're under pressure, under sanctions to come to the table, to go on a kind of charm offensive," Rice said. "In fact, I think… former Secretary Tillerson actually deserves a lot of credit for putting together a pretty tough isolation campaign."

She also said she was "impressed" then-CIA Director Mike Pompeo, who is now secretary of state, was able to visit North Korea's capital in secret. "This could be an opening. This is the first time we've dealt this directly," Rice said.

For verification of denuclearization, Rice advocated for "snap inspections" with North Korea who has cheated on agreements in the past.

"Meaning that you can go anywhere, any time that you wish to send inspectors there. These regimes are very good at, for instance, cleaning up a site after they've been notified that you want to look at that site. And so they tend to list their known sites, but hide other sites. And so you have to be able to go anywhere, anytime," Rice said.

She added that inspectors on the ground make a difference.

"I hope that one of the first steps in these North Korean negotiations would be to get inspectors, International Atomic Energy Agency inspectors, on the ground. Because our intelligence about North Korea is not very good," Rice said. "Being on the ground with experienced people, you pick up things that you wouldn't be able to pick up through other means."

Rice also said she's not worried the North Korean negotiations will be impacted by Mr. Trump's looming decision on the Iran nuclear deal, an accord she said was a "weak agreement" that she would not have signed.

"The North Koreans are going to negotiate, if they negotiate, because it's in their interests to do so because they're under pressure," Rice said. "What has happened with Iran I think isn't the issue. It might be a little bit of an object lesson though for Kim Jong Un that we negotiated with [Libyan dictator] Muammar Qaddafi, and Qaddafi didn't end up so well. I think that may be more in his memory bank than what we do with Iran."