Asked whether he would rule out the United States boarding and inspecting North Korean ships, Mnuchin said, "No, I can not rule that out".
U.S. officials and some analysts suspected that North Korea was creating an inter-Korean thaw to soften its image and weaken worldwide sanctions.
The delegation plans to return to North Korea on February 27.
CBS News reported the South Korean presidential office released a statement on the subject, saying the North had "ample intentions of holding talks with the United States".
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Kim Yong Chol's nomination as leader of the visiting delegation is controversial in the South, where he is widely blamed for attacks including the torpedoing of Seoul's Cheonan warship in 2010 with the loss of 46 lives.
Prior to the kosher feast, President Moon Jae-in presented Trump with red embroidered slippers and two special-edition stuffed animals. On Saturday, North Korea's state-run media said that its nuclear weapons were only aimed at the USA and were only meant to establish peace on the Korean peninsula.
After the aborted meeting during the opening, there was speculation about a working-level meeting between United States and North Korean officials.
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Both leaders expressed disappointment over the political impasse at Stormont. Mandatory coalition is not sustainable in the long term.
Ivanka Trump's appearance at this weekend's closing ceremony of the Pyeongchang Olympics on behalf of the White House and the United States is a softer bookend to Vice President Mike Pence's awkward visit during the opening ceremony.
It's possible the USA and North Korea delegations could come into close contact in the VIP Box in the PyeongChang Olympic Stadium during the final theatrics of a Winter Olympics that is winding down after 16 days.
On Sunday, South Korea confirmed another interesting name on the list: Choi Kang Il, the deputy director of the North American affairs.
A North Korean delegation headed by a former intelligence chief has been greeted by protests as it crossed into South Korea to attend the closing ceremony. According to the USA, a planned meeting between the delegations from Washington and Pyongyang the following day was canceled at short notice by the North Koreans.
Kim Yo Jong and the North's nominal head of state were the most senior North Korean officials to visit the South in more than a decade.
She sat in the same VIP box with Moon and U.S. Vice President Pence, creating some awkward moments. Pence's office claimed afterward that the North pulled out of a planned meeting at the last minute.
U.S. President Donald Trump, in announcing the new sanctions on Friday, warned of a "phase two" that could be "very, very unfortunate for the world" if the sanctions did not work.
In the USA, he added, "We stand up to murderous dictatorships". A statement carried by KCNA said that Trump should know the North would "never have face-to-face talks. even after 100 years or 200 years" with those who had been "viciously slandering the dignity of our supreme leadership".