"North Korea's not going to change the way they do business unless they believe that the military option's on the table", Graham, R-S.C., said on "Sunday Morning Futures".
Despite the unprecedented rapprochement between the two countries, the North Koreans have maintained a tight security presence around their leader.
Trump Kim Summit
The document signing followed a series of meetings at a luxury Singapore resort.
Reacting to the news of the two leaders meeting, basketball star and unlikely North Korea envoy Dennis Rodman, who is also in Singapore, said holding the summit was the right thing to do.
As the historic first meeting between a sitting U.S. president and North Korean leader began in Singapore, images of Trump and Kim exchanging handshakes and warm words drew jubilant reactions in Seoul and hopes for a new beginning with Pyongyang.
"Yes, Donald Trump reached out", Rodman said, telling Cuomo he'd received a call from a person he described as Trump's secretary.
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President Trump gives North Korea leader Kim Jong Un a thumbs up at their meeting on Sentosa Island in Singapore on Tuesday.
He expressed hope that Trump and Kim would be able to make progress. Adding that meet was "very, very, very good", Trump said both the countries have an "excellent relationship".
Members of the U.S. delegation, including USA secretary of state Mike Pompeo, right, and John Bolton, national security adviser, left, and North Korean advisers watch a television screen showing the meeting. And that suggests, perhaps, a confidence level on the North Koreans that this summit might go well.
And until denuclearisation takes place, sanctions against North Korea would remain in place, he stressed.
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Garrett also asked the president about verifying North Korean compliance.
The president is set to meet with North Korean leader Kim Jong Un on June 12 in Singapore.
"I hope that a major agreement on ending hostile relations (between USA and North Korea) and the denuclearization of the Korean Peninsula is reached through this time's summit", Moon said.
A complete, verifiable and irreversible denuclearization "is the only outcome that the United States will accept", Pompeo told reporters on Monday evening in Singapore.
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The U.S. will move to tighten the punishing measures if diplomacy fails, he added.