Albright, who served during the Bill Clinton presidency, told CNN's Jake Tapper on "The Lead" that she was surprised by Trump's remarks
to Bloomberg News earlier this week, in which the President said he'd be "honored" to meet with Kim "under the right circumstances."
"A president doesn't go to a country without any preparation, and 'honored' would definitely be the wrong way to discuss somebody who is keeping his people in poverty and starving and control," Albright said Tuesday.
She warned that Trump shouldn't think of his relationship with the dictator as a personal one.
"I think that part of the issue is that President Trump seems to believe that he can have just one-on-one relationships. And maybe that's possible in business, but that is not something that is possible as president of the United States," she said. "This is not a matter of charming, by saying you're 'honored' and he's a 'smart cookie.'"
Albright is one of the most high-profile
American diplomats to have visited North Korea on official business, meeting with former North Korean leader Kim Jong Il in Pyongyang in 2000. But no sitting US president has ever met with the leader of North Korea while in power, and the idea is extremely controversial.
Asked what her advice to Trump would be, Albright said: "I do think it's important to push them, and the Chinese can be more helpful on this -- and we have to make it clear that they cannot be a nuclear power."
The former secretary of state stressed open communication between the Trump administration and Russia, acknowledging that she believes it "certainly looks" like relations between the United States and the Kremlin are at their worst levels since World War II.
"I do think it's important to have a functional relationship with Russia, to tell them what's acceptable and what's not. I think the phone calls are fine," she said of Trump's relationship with President Vladimir Putin.
Trump had a call
with Putin on Tuesday.
Trump's relationship with Russia has been highly scrutinized, especially in the wake of news that the FBI is investigating Russia's involvement in hacking
of Democratic servers and Democratic presidential candidate Hillary Clinton's campaign prior to the election.
At the time, FBI Director James Comey announced the FBI was looking into investigating Clinton's use of a private email server. The bureau ultimately decided not to reopen an investigation into Clinton, but many
, including Albright, believe Comey's comments shortly before the campaign's end contributed to Clinton's loss.
"I was out on the road and I know the Comey letter made a difference. I saw that," Albright told CNN. "As I was out and about, people would ask a lot about it and it would raise questions that as it turns out that were unnecessary. I think (Clinton) did the right thing in taking responsibility (for the loss), but there were outside factors in Comey and what the Russians were doing."