"Discussions are ongoing and they're going very, very well", Trump told reporters.
The North Korean officials were being recalled for a possible ambassadorial meeting, according to South Korea's Yonhap News Agency.
"I think in the next couple weeks we will have the first remains returned", Pompeo said during a meeting at the White House. "We will be ready".
Kim's meeting with the North Korean senior official is seen as part of an effort to strengthen bilateral cooperation through projects related to their shared history of the colonization of the Korean Peninsula. They have no time limit for this and no need to rush the process is very quickly. The U.S. State Department announced earlier in the day that it will take action against entities that are found to have helped Pyongyang evade global sanctions.
However, the timing of the handover and the number of sets remains to be returned is still uncertain, in spite of two days of talks between United States and North Korean officials on Sunday and Monday, said the official, who did not want to be identified.
"Our government has been taking necessary diplomatic efforts to closely cooperate with the worldwide community and the [UN Security Council] Sanctions Committee on the faithful implementation of UN sanctions resolution on North Korea", said Noh Kyu-duk, spokesman of the Ministry of Foreign Affairs in Seoul Tuesday, following reports of the illegal coal shipment entering South Korean ports. North Korea said that an August reunion of Korean families separated by war may not happen if South Korea doesn't immediately return some of its citizens who arrived in the South in recent years.
On Wednesday, Trump reaffirmed in a tweet that Russian Federation "had agreed to help with Noth Korea", adding sanctions he extended on Pyongyang earlier in April would remain in place. However, Pyongyang shouldn't look forward to an easing of sanctions any time soon, as, according to Trump, they will remain in place.
The prosecutor's office suspects that Lee leaked 109 pieces of classified information, including personal data of South Korean intelligence operatives working in foreign legations overseas who have had to leave their posts and return after the case came to light.
After Pompeo's visit, North Korea accused his delegation of making "gangster-like" demands in connection with denuclearization.
"There are no missing Americans who have been "already identified" by the DPRK (North Korea) to be repatriated", says Paul Cole, who has researched POW-MIA issues from the Korean War for decades and served for four years as a scientific fellow at the Pentagon's Central Identification Laboratory in Hawaii.
Mr Trump said on Tuesday that talks with Pyongyang were going fine.
National Security Adviser John Bolton said more recently that Washington has a plan that would lead to the dismantling of the North's nuclear and missile programs in a year.