Pompeo did not confirm media reports that the first repatriations would be on July 27, and that about 50-55 sets of remains would be returned.
Trump had said he and Putin discussed reducing nuclear weapons worldwide.
The text has been criticized for the lack of specifics and deadlines regarding the dismantlement of the North Korean nuclear programme.
The U.N. Security Council has unanimously boosted sanctions on North Korea since 2006 in a bid to choke off funding for Pyongyang's nuclear and ballistic missile programs, banning exports including coal, iron, lead, textiles and seafood, and capping imports of crude oil and refined petroleum products.
According to reports, Pyongyang has agreed to fly the remains out of their country within the next two weeks, following two days of discussions with US military officials. There is no rush, the sanctions remain! The global community will end up having little choice but to accept North Korea as a nuclear power.
U.S. officials have previously said it could take years to identify all the remains and to determine whether they are, in fact, Americans.
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"It's unpredictable what kind of communication would happen before President Moon's visit to Pyongyang", South Korean Foreign Minister Kang Kyung-hwa told reporters in London on Wednesday, following her meeting with ambassadors based in Europe, Yonhap reported.
Also, North and South Korea agreed to sign a peace treaty formally later this year, ending a 65-year-old long war between them.
Russia's RIA news agency, citing Moscow's envoy to Pyongyang, reported on Wednesday that a summit between the leaders of Russian Federation and North Korea is "on the agenda" and that it would be "logical" to raise the idea of lifting sanctions.
Broadcaster Voice Of America reported Tuesday that an expert panel under the United Nations sanctions committee found that North Korea shipped coal to the Russian port of Kholmsk on Sakhalin Island. six times between July and September 2017.
On Tuesday Trump said he had misspoken and that he had complete faith in USA intelligence agencies and accepted their conclusions.
As Mark Fitzpatrick of the International Institute for Strategic Studies put it in a web essay last week, "What was supposed to be the easiest item on the United States-North Korea negotiations agenda - the return of Korean War soldiers' remains - is proving to be yet another sticking point".
Earlier North Korea participated in 2018 Winter Olympics in Pyeongchang, South Korea along with a high power delegation headed by sister of Kim Jong-un.