North Korean leader Kim Jong-un with US President Donald Trump.
South Korean Foreign Minister Kang Kyung-wha told reporters afterward that the military drills issue "was not discussed in depth".
Mr Pompeo also said the U.S. wants North Korea to take "major" nuclear disarmament steps before the end of Mr Trump's first term in 2021.
Putin said he would like to welcome Kim Jong-un to Russian Federation, suggesting they meeting during an economic forum in the far eastern port city of Vladivostok this September.
The meeting between Donald Trump and Kim Jong-un has reduced the risk of a large military conflict on the Korean Peninsula, according to Putin.
However, South Korean President Moon Jae-in told Pompeo the summit had helped the world "escape the threat of war, nuclear weapons and missiles".
Pompeo, speaking in South Korea after the summit, wouldn't budge on the possibility of sanctions coming off in phases, as both Mr. Trump and the North Koreans have suggested.
Also on Thursday, North and South Korea held their first military talks in more than a decade.
This did not stop the United States president from talking up the outcome of what was the first meeting between a USA and North Korean leader in six decades of hostility.More news: Justice report expected to slam Federal Bureau of Investigation actions in Hillary Clinton email case
US Secretary of State Mike Pompeo (L) shakes hands with Chinese Foreign Minister Wang Yi before their meeting at the Great Hall of the People in Beijing on June 14, 2018.
As an "important party", China offered to assist North Korea and the USA in further talks and in implementing decisions made at the summit.
There has been deep scepticism about the agreement, with observers saying it lacked detail on how North Korea would give up its nuclear weapons and how that process would be verified.
"We're going to get denuclearisation", Mr Pompeo said. Wang said the US should continue to "work through China".
Trump has been under fire for his friendliness towards North Korea..
Hailing the continuously developing U.S.
Meanwhile, Japanese Prime Minister Shinzo Abe was mulling his own summit with Kim in August or September, the Yomiuri Shimbun reported, citing several unidentified government officials.
But they were effectively postponed when North Korea, angered at a U.S.
After meeting with Kim, many were surprised when Trump spoke about joint military exercises, what he called "war games", with South Korea.
The United States appreciates China's vital role in the political settlement of the Korean Peninsula nuclear issue, he said, adding that the United States is willing to work with China to promote realization of denuclearization and lasting peace on the peninsula.