"A USA delegation is in ongoing talks with North Korean officials at Panmunjom", State Department spokeswoman Heather Nauert said in a statement, referring to the truce village in the demilitarized zone between the Koreas.
The North Korean team in Panmunjom is led by Ms Choe Son Hui, a vice-foreign minister whom Mr Sung Kim has dealt with many times before - most notably when she was deputy director of the North Korean Foreign Ministry's North American Affairs Bureau and was involved in the 2003 to 2009 six-party talks to denuclearise North Korea.
His remarks came as South Korean President Moon Jae In said yesterday that Mr Kim was still committed to denuclearisation after their surprise meeting on Saturday.
A team led by Sung Kim, a former American negotiator with North Korea who now serves as ambassador to the Philippines, is holding another round of talks Tuesday on the northern side of the demilitarized zone that separates the two Koreas.
A Kim Jong Un impersonator poses for a selfie with tourists at Merlion Park in Singapore on May 27, 2018. "I'd like to say that the fact that North Korea and the USA agreed to have a summit and working-level talks indicates that the US has already confirmed the North's intentions".
The South Korean leader is optimistic that relations with North Korea will continue to improve, saying, "If we could hold working-level, back-to-back talks on both sides of Panmunjom if urgently necessary in addition to formal summits, it would expedite advancement of inter-Korean relations".
"With South Korea and China already talking to the North, it's hard for Trump to reignite his campaign at this point or after the summit fails", said Namkoong Young, who has advised South Korea's Unification Ministry and the Foreign Ministry on policy for nearly 10 years.
"The president and prime minister affirmed the shared imperative of achieving the complete and permanent dismantlement of North Korea's nuclear, chemical and biological weapons and ballistic missile programmes". He said he expects the talks to go smoothly because Pyongyang and Washington both know what they want from each other.
At the same time, a team of US government officials left US Yokota Air Base in Japan for Singapore on Monday, NHK said.
Mr Trump withdrew from the planned summit last week, but quickly announced it could get back on track.
Pentagon official Randall Schriver was part of the U.S. team, the official said.
Despite repeated references to "denuclearization of the Korean Peninsula" by the North, it remains unclear whether Kim will ever agree to fully abandon his nuclear arsenal.
South Korea was caught off guard by Trump's abrupt cancellation of his summit with Kim, with the US president citing hostility in recent North Korean comments. South Korea and China account for nearly all of North Korea's land borders, so their support is essential for enforcing sanctions ramped up past year after Mr Kim declared the ability to strike the United States with a nuclear weapon.
Mr Trump had rattled the region on Thursday by cancelling his meeting with Mr Kim, citing "open hostility" from the Pyongyang regime.
During Moon and Kim's second border meeting Saturday the two leaders exchanged views on how to prepare for the North's possible summit with Trump. The North Korean leader could now "continue to play nice in public but stall out the process behind closed doors", said Mount, of Federation of American Scientists.