After a three-way meeting with Mr Pompeo and Japan's top diplomat, South Korean foreign minister Kang Kyung-wha suggested the United States still had some explaining to do, telling reporters that the issue of the drills "was not discussed in depth".
"The meeting of the century awaited by the whole world finally took place" on Tuesday, the voiceover said to shots of Kim's long motorcade en route to the summit venue on Sentosa island.
He stressed that the meeting between President Trump and Kim Jong Un, top leader of the Democratic People's Republic of Korea (DPRK), was historic, fruitful and an important step in the process of a political settlement of the peninsula nuclear issue, saying China extends heart-felt congratulations to both sides. It will be treated as a military victory by the North Koreans.
The televised account of this week's summit had an epic air, using triumphant music to underscore its gravitas - perhaps a fitting stylistic touch for the first-ever meeting of sitting leaders of the United States and North Korea, despite recent tensions.
US Secretary of State Mike Pompeo, right, Japanese Foreign Minister Taro Kono, center, and South Korean Foreign Minister Kang Kyung-wha.
As an "important party", China offered to assist North Korea and the U.S. in further talks and in implementing decisions made at the summit. The statement came despite the lack of concrete proof that North Korea will discontinue its nuclear program.
Pompeo said he doesn't know the exact timing.
He declared there was "no longer a Nuclear Threat from North Korea" and that he could see "great potential" in the country.
He also had a sit down with Chinese President Xi Jinping before heading back to the U.S.
The president made the comments after his meeting with Kim.
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.
Observers expect a visit by a North Korean official to Beijing soon, as the traditional allies will want to consult going forward.
In Japan and South Korea, there is growing bewilderment over the fact that Trump expressed his intention to consider suspending U.S.
According to a Reuters/Ipsos poll, over half of Americans approve of how Trump has handled North Korea, but only a quarter think the summit will lead to the denuclearization of the Korean Peninsula.