Pompeo told a Cabinet meeting chaired by U.S. President Donald Trump that progress was made on some issues when he visited Pyongyang earlier in July for the third time this year, but a lot of work remained to be done.
The repatriation of remains of soldiers killed in the Korean War was one of the agreements reached during the June 12 summit between Trump and North Korean leader Kim Jong Un in Singapore.
"We're making progress along the border to get the return of remains - a very important issue for those families," Pompeo said. "We think in the next couple weeks we'll have the first remains returned. That's the commitment."
U.S. and North Korean officials met on the inter-Korean border on Sunday to discuss the return of remains.
It was the first time in nine years that U.S. and North Korean generals held talks. The two sides agreed to resume joint field activities to search for the remains of Americans missing from the war, Pompeo said in a statement on Sunday.
Pompeo also said on Wednesday the North Koreans had "reaffirmed their commitment to denuclearize." He did not elaborate.
After Pompeo's visit, North Korea accused his delegation of making “gangster-like” demands in connection with denuclearization.
(Reporting by Roberta Rampton, writing by Doina Chiacu; editing by Jonathan Oatis and James Dalgleish)