US President Donald Trump has said talks with North Korea could take place "over the next three or four weeks".
"It's going [to] be a very important meeting, the denuclearisation of the Korean peninsula," he said.
Meanwhile, new Secretary of State Mike Pompeo said he had had a "good conversation" with North Korea's leader Kim Jong-un in Pyongyang recently.
On Friday, Mr Kim and the South Korean President Moon Jae-in agreed to work to rid the peninsula of nuclear weapons.
The inter-Korean summit at the border came just months after warlike rhetoric from the North.
Mr Kim became the first North Korean leader to set foot in South Korea since the end of the Korean War in 1953.
For years, Pyongyang has insisted that it would never give up its nuclear arsenal, which it claims it needs to defend itself against aggression from the US.
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