By Sarah N. Lynch

WASHINGTON (Reuters) - U.S. Secretary of State Mike Pompeo said on Sunday that Washington would agree to lift sanctions on North Korea if the country agrees to completely dismantle its nuclear weapons program, a move that would create economic prosperity that "will rival" that of South Korea.

As Pompeo spoke on several Sunday morning talk shows, the Pentagon said three American prisoners freed by North Korea had left Walter Reed National Military Medical Center in Washington and been reunited with their families.

President Donald Trump and North Korean's Kim Jong Un

have a planned June 12 meeting in Singapore, the first such encounter between a sitting U.S. president and a North Korean leader.

Pompeo said the United States would not be willing to invest taxpayer dollars to help the country, but was willing to "lift sanctions" to pave the way for private American investment in North Korea’s energy, agriculture and infrastructure sectors.

“What Chairman Kim will get from America is our finest – our entrepreneurs, our risk takers, our capital providers. ... They will get private capital that comes in. North Korea is desperately in need of energy ... for their people. They are in great need of agricultural equipment and technology,” he said on CBS' “Face the Nation.”

“We can create conditions for real economic prosperity for the North Korean people that will rival that of the South,” he added.

North Korean state media reported over the weekend that the country had scheduled the dismantlement of its nuclear bomb site for later in May.

Pompeo welcomed that news.

"Every single site that the North Koreans have that can inflict risk on the American people that is destroyed, eliminated, dismantled is good news for the American people and for the world," he said on "Fox News Sunday."

Video: NK to Dismantle Nuclear Test Site, State Media Reports

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COULD BECOME 'NORMAL NATION'

Last month, Pompeo became the first known U.S. official to meet with Kim, where he helped lay the groundwork for the upcoming meeting with Trump.

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He returned again to North Korea last week for a second meeting, after which Kim agreed to the release of the three Americans.

Lieutenant Colonel Mike Andrews, a Defense Department spokesman, described former prisoners Kim Dong-chul, Kim Sang-duk, who is also known as Tony Kim, and Kim Hak-song as being "grateful, in good spirits and coping well" when they left the hospital after medical evaluations.

"The returnees have been reunited with their families. Their time together has been an incredibly joyous occasion. They ask for privacy as they transition home," Andrews said.

White House national security adviser John Bolton said on CNN's "State of the Union" on Sunday that North Korea's future could be "unbelievably strong" if it follows through on its commitment to denuclearize.

"The prospect for North Korea is for it to become a normal nation, to behave and interact with the rest of the world the way South Korea does," he said.

Pompeo spoke about what it was like to meet Kim, whom few Americans have interacted with personally.

"The conversations are professional," he said on "Fox News Sunday. "He does follow the Western press. He'll probably watch this show at some point."

(Reporting by Sarah N. Lynch; Additional reporting by Valerie Volcovici, Idrees Ali and David Morgan; Editing by David Gregorio and Peter Cooney)