The meeting was expected to be the first working-level talks between the two sides since Pompeo's visit to Pyongyang ended Saturday with North Korea denouncing the U.S.'s "unilateral and gangster-like demand for denuclearization".
The letter, sent on July 6, was unveiled exactly a month after Trump and Kim's historic summit in Singapore.
Returning the remains was a commitment from the 12 June summit between Kim Jong-un and Donald Trump in Singapore.
A USA official waited at the border of the village but no North Korean official showed up, according to South Korea's Yonhap news agency.
Trump has expressed an eagerness to tout the recovery of the war dead, telling Fox News that Kim was "giving us back the remains of probably 7,500 soldiers".
And even as Trump released Kim's note, the USA was asking the UN Security Council to punish North Korea after finding that Pyongyang had violated restrictions on refined oil imports.
"Just heard Foreign Minister of North Korea speak at U.N. If he echoes thoughts of Little Rocket Man, they won't be around much longer!"
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He wrote: "I deeply appreciate the energetic and extraordinary efforts made by Your Excellency Mr President for the improvement of relations between the two countries and the faithful implementation of the joint statement".
But readers soon pointed out that the letter didn't actually mention any action that had been taken, and only made vague promises about 'the future progress of taking practical actions'.
Although KCNA did not say when the trip was made, Kim Yong Chol told a visiting Seoul official last week that the leader was away for a trip to a "local region".
Trump agreed to halt bi-annual USA military exercises conducted with South Korean forces, while Kim made a vague commitment to denuclearization. The meeting was about returning the remains of American soldiers from the Korean War.
Pompeo called the talks "productive", although North Korea said it was disappointed with the emphasis on denuclearization with a lack of security guarantees.
Pompeo had said a Pentagon team would meet with the North's officials on or around Thursday at the inter-Korea border to discuss the repatriation.
"We were ready", the official said.
At high-level talks last week, North Korea and the US confirmed they are still poles apart on the next steps to be taken in the process.
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