"He has not curbed his use of nuclear weapons and missiles as he said he would," former U.S. ambassador to the UN Bill Richardson said.
Trump became the first U.S. president to set foot in North Korea on Sunday when he crossed the border with Kim.
"That's news to me," said James Clapper.
The demilitarized stretch of land acts as a buffer between North and South Korea, and has become a de facto wildlife sanctuary.
The 25-year-old said that many North Koreans are "indifferent" to Kin Jong Un's leadership and feel no loyalty to him.
Seoul called the move "positive from a humanitarian perspective."
The two Korean leaders agreed last Friday to cease the launch of propaganda leaflets across the border.
The loudspeakers were switched off for the first time in two years.
The first such meeting in 11 years will take place in April.
The National Intelligence Service briefed the South Korean National Assembly's intelligence committee on an investigation into the soldier's motives for defecting.
South Korea had a record-low level of North Korean refugees arriving in the country.
After the world's deadliest conflict, a future secretary of state decided to split North and South Korea based on a map he found in a magazine.
Jenkins had been in North Korea for 15 years when the regime brought Hitomi Soga to live with him.
The North Korean defector's life was saved by doctors after he fled across the DMZ last month.
Doctor Lee Cook-Jong said the 24-year-old had a nightmare about being abducted and taken back to North Korea.
A diplomatic delegation including the top U.S. diplomat in South Korea visited the JSA on Wednesday.
The guards were replaced and possibly punished, a South Korean intelligence source told local media.
The soldier is going to survive his injuries, doctors said on Wednesday.
A South Korean law allows the country to deport foreigners if they pose a threat to security or public interest.
The facility was recently expanded at a cost of around $11 billion, largely contributed by the South Korean government.
The U.S. president is reportedly considering visiting the border area splitting the Korean peninsula on his tour of Asia.