President Trump shared a letter from North Korean leader Kim Jong-un on Thursday, praising the work being done with that country.
Several days previously, Pyongyang had slated the USA for seeking unilateral and forced denuclearization from North Korea.
In the meeting at the Korean Peninsula's demilitarized zone, the two sides had been expected to discuss the return of US troops' remains from the 1950-53 Korean War - an arrangement that the State Department had announced after Secretary Michael R. Pompeo's visit to Pyongyang last weekend.
"We will be ready", Nauert said.
The fact that North Korea seem to be dragging its feet on this issue fuels already growing doubts among President Trump's critics about whether the Singapore summit was a success or simply a publicity stunt for Mr Kim, the BBC's Cindy Sui in Seoul reports.
Trump later said North Korea was no longer a nuclear threat, even though no details were announced, and critics suggested the president had failed to secure any new commitments from Pyongyang toward the dismantling of its nuclear missile program.
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The government has reportedly struggled to offer exact information about the number of children separated from their parents. For almost one month Perez knew nothing about her children - "the longest, most torturous time of my life", she said.
"The US is fatally mistaken if it went to the extent of regarding that the [Democratic People's Republic of Korea] would be compelled to accept, out of its patience, the demands reflecting its gangster-like mindset", Pyongyang cautioned.
Pompeo insisted that a raft of tough economic sanctions imposed on North Korea would remain in place until "final, fully verified denuclearisation" occurs.
Trump has touted the return of remains as one of the successes of his historic June 12 summit with Kim.
But U.S. Defense Department and United Nations Command officials were left waiting in the DMZ's Joint Security Area, with no immediate explanation for the North Korean absence, according to South Korean's Yonhap news agency and U.S. officials who spoke to CNN and The Washington Post.
North Korean and United States teams, as well as UN officials, had been due to discuss the details of repatriation.
According to the Pentagon, North Korean officials have indicated in the past that they have the remains of as many as 200 United States troops. "I have it for him", Trump said.
What's next for Secretary of State Pompeo's negotiations with North Korea?
If realized, they will be the first general-level military talks between North Korea and the UNC since March 2009.