Pompeo had flown to North Korea to gather the three men and escorted them home on a plane back to the U.S. "When I say victims, I am implying that they were subject to some kind of deceit in regard to where they were going".
USA forces brought some 100 wooden coffins into the DMZ last month, which will be used to transport the remains, according to Yonhap.
Pompeo claimed that a "great deal of progress" was made during talks, however, North Korea's foreign ministry called the meeting "regrettable", describing the USA attitude as "cancerous".
The discussions, which took place in the demilitarized zone between the Koreas, follow a commitment made by the North during the June 12 summit in Singapore to recover the remains of USA prisoners of war and those missing in action and immediately repatriate the remains of those that have already been identified.
Pompeo initially said the two sides had agreed to hold talks on US remains on Thursday but no North Korean representatives showed up at the border. It is the first time in more than nine years that the discussion has focused on returning the remains of US soldiers.
"One can only speculate on why it happening now - but it seems that after the political situation surrounding North Korea calmed down, Kim switched his attention from diplomacy to the economy and the on-the-spot guidance - and he is not pleased".
Pompeo sharpens tone on North Korea
After entering disarmament talks with the United States earlier this year, Kim met in June with U.S. President Donald Trump and agreed to commit to "complete denuclearization of the Korean Peninsula".
The Korean War raged from 1950 until 1953, though it ultimately ended with a ceasefire agreement rather than a formal peace treaty, meaning it is still technically ongoing.
About 7,700 US soldiers are listed as missing from the Korean War.
The European Union should not lift sanctions against North Korea until the country has fully denuclearized, the High Representative of the EU for Foreign Affairs and Security Policy said on Monday.
State Department spokeswoman Heather Nauert said on last Saturday that Pompeo had handed Kim a letter written by Trump, meaning that Kim's letter may have been a response to the US President, a few hours before the North Korean government denounced Washington for its "unilateral and gangster-like demand for denuclearization". The U.S.is demanding both countries cut North Korea off completely.
About 7,700 USA soldiers are listed as missing from the Korean War, and 5,300 of the missing are believed to be in North Korea.
But efforts to recover and return other remains stalled for more than a decade because of the North's nuclear weapons development, which led the U.S.to claim that it could not guarantee the safety of recovery teams it sent during the administration of former President George W. Bush.