Kim Yong-nam conveyed Kim Jong Un's "sincere regards" and "absolute support of the people of Russian Federation", handing a personal message to Putin from the North Korean leader.
Pompeo is meeting with the Japanese and South Korean foreign ministers in Seoul.
"When we refer to the mistakes of the past". That is not going to happen.
Al Jazeera's Wayne Hay, reporting from Seoul, said that the meeting was an opportunity for the three countries "to show that they are in the same page" when it comes to the issue of North Korea and denuclearisation.
The three-way meeting comes as USA allies and South Korea seek more details about Trump's unprecedented nuclear summit with Kim in Singapore on Tuesday and what's next for US nuclear negotiations with the North.
North Korean state media reported on Wednesday that Kim and Mr Trump had recognised the principle of "step-by-step and simultaneous action" to achieve peace and denuclearisation on the Korean peninsula.
China's state-run Xinhua news agency said Taiwan came up in Pompeo's meeting with Xi.
One reporter pressed Pompeo on the agreement not containing more precise language on CVID ("complete, verifiable, irreversible denuclearization", as the State Department put it earlier this week).
North Korea blamed botulism and ingestion of a sleeping pill and dismissed torture claims.
Trump said the United States would stop military exercises with South Korea while North Korea negotiated on denuclearisation.
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He also had a sit down with Chinese President Xi Jinping before heading back to the U.S.
"The South Koreans didn't know about it".
He bristled at questions from reporters about the vague wording of the statement where North Korea "commits to work toward complete denuclearisation of the Korean Peninsula" - a promise it has made several times before in the past 25 years and reneged on.
National Security Adviser and retired soldier Paul D Eaten, who served more than 30 years in the USA army said the move was "wholly inappropriate for the Commander in Chief".
In a statement, U.S. Forces-Korea said it had received no guidance or forewarning of Trump's announcement of the halt to the exercises, and South Korea professed to be baffled.
President Donald Trump saluted North Korean general and defense minister No Kwang Chol during the Singapore summit, as seen in a video released by the country's state media.
Japanese Foreign Minister Kono was more cautious in his praise.
Human rights activists - and the US government - have also admonished the North Korean regime for its long record of detaining and punishing thousands of people in prison camps.
The U.S. and South Korea typically hold a number of large-scale joint military drills every year, including Foal Eagle/Key Resolve (FE/KR) in March and April and Ulchi Freedom Guardian (UFG) in August. "But I think we understand each other".
"Right now, the USA and South Korea are not engaged [on troop withdrawal], and we're the only ones who make up our mind on this", he said.
But the document has been criticised for lacking details on when or how Pyongyang would give up its weapons.