Media captionTrump Kim summit: Win-win, or a Kim win?
At the US military command in South Korea, officials also reacted with uncertainty.
Mr. Cronin suggested Mr. Trump had not made a major concession. Trump, it added, had expressed his "understanding" of the stance and had conveyed "his intention to halt" the exercises.
"I showed it because I really want him to do something", he said.
The historic agreement came after the two leaders held several meetings throughout the day.
He paused for a moment, then added: "I don't know that I'll ever admit that".
In a statement sent to the BBC, she said: "Our alliances remain ironclad, and ensure peace and stability in the region". The video offered Kim a stark choice between military conflict on the Korean Peninsula and the kind of robust economic development that has turned neighbouring South Korea into a wealthy nation.
Trump's pledge to end joint exercises with South Korea without explicit concessions from North Korea to lower the military threat posed by Pyongyang took South Korean and USA military officials by surprise.
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What are the war games?. "There were obstacles but we overcame them to be here".
After the summit, Trump said the process of repatriating remains would begin immediately.
The newspaper's coverage was largely framed around the premise that it was Trump who was most eager for the summit.
Kim has managed to build upon the work of his father and grandfather and secured the highest form of recognition that there is - a bilateral meeting with the president of the most powerful country on the planet.
On nuclear weapons, Mr Kim "reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean peninsula". Details of the document are not yet clear. Now that we meet and have a great relationship with Kim Jong Un, the same haters shout out "you shouldn't meet, do not meet!"
In addition to his one-on-one with Trump, Kim also impressed observers in "four-by-four" talks, enlisting former spy chief Kim Yong-chol, Foreign Minister Ri Yong-ho and vice-chairman of the Workers' Party of Korea Ri Su-yong for discussions.
While President Trump might be correct that his threat to rain "fire and fury" on the Korean Peninsula helped get Kim to the table (and perhaps persuaded Xi to cajole him there), the opportunity to convert that leverage into real denuclearization has been squandered.
Trump called the North Korean leader "worthy", "smart" and "talented" after the Singapore summit while days earlier describing Trudeau as "dishonest and weak" following a G7 summit in Quebec.