U.S. President Donald Trump and North Korea's leader Kim Jong Un meet in a one-on-one bilateral session at the start of their summit at the Capella Hotel on the resort island of Sentosa, Singapore June 12, 2018.
The North has long accused the U.S. of provoking the 1950-53 Korean War as part of a plan for global domination and blames it for the division of the peninsula, agreed between Moscow and Washington in the closing days of World War II.
Referring to Trump's decision to suspend United States military exercises in the region, Pompeo said that "the President was clear".
North Korean leader Kim agreed to resume the recovery efforts in his summit with President Trump earlier this month in Singapore.
The prime minister also said at the ceremony the United States and South Korea have chose to suspend joint military exercises and the North and South agreed to reunite 100 individuals from each side during a family reunion late August.
Speaking to CNN in a telephone interview conducted on Sunday and reported by the network on Monday, Pompeo said he wanted to see continued progress toward North Korean denuclearization and that the administration would regularly assess Pyongyang's seriousness about abandoning its nuclear program.
"We hope that we will have an ongoing process of making progress", CNN quoted him as saying.
The Pentagon says Pyongyang has indicated several times that they have as many as 200 sets of remains that could be those of USA soldiers who died in the war.
At the Singapore summit, the first meeting between a serving US president and a North Korean leader, Kim reaffirmed a commitment to work toward complete denuclearisation of the Korean peninsula, while Trump said he would halt joint U.S.
The US is sending 215 coffins to North Korea to bring back the remains of American soldiers in a follow-up to a summit agreement between Donald Trump and Kim Jong-un. Each of the actions we have taken, his decision to suspend the high level war games, it's only so long as there is a good faith negotiation progress, productive results being achieved.
In the joint statement, Kim "reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula", but made no reference to a timeline, and going into the summit, Pyongyang repeatedly rejected unilateral nuclear disarmament.
"It's remarkable", said Peter Ward, a North Korea researcher at Seoul National University.
Less than two weeks after the summit, Pompeo suggested it was too soon to expect a detailed roadmap after 40 years of tensions between the two countries.