There has been no decision on large scale drills scheduled for early next year, Mattis said.
North Korea believes Trump made the same promise - to declare an end to the war - to Kim Yong Chol, a top North Korean official close to Kim Jong Un, at the White House on June 1 - 11 days before the summit, Vox also reported.
"We suspended several exercises at the direction of the president", Mattis said.
United States defence secretary James Mattis.
"We have not made decisions on that at this time and we'll do that in consultation with state", said Mattis, suggesting that the State Department would have a say depending on how talks with North Korea are progressing.
Trump also used the term after his meeting with Kim when he announced the USA was suspending what he called "war games".
After the conclusion of the June summit, Trump declared that North Korea was "no longer a Nuclear Threat".
South Korea, U.S. reaffirm commitment to North Korea's fully verified denuclearization
It appealed to both sides to "show more sincerity and flexibility" instead of "being capricious and overly prejudiced". Mattis believes that issuing such a declaration without thinking through all implications could negatively impact U.S.
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Aaron Ramsey nodded in the rebound but was flagged offside, before West Ham broke and Arnautovic arrowed an effort into the side-netting.
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I think it's easier for the offensive players. "I think this lad has to go for his own sake and say "I need to go, I need to go and play".
Following the Singapore summit, the military suspended the massive Ulchi Freedom Guardian exercise in South Korea, which involves thousands of American troops each year. But the US government has not yet decided whether to hold Ulchi Freedom Guardian in 2019. -South Korea joint live-fire military exercise, at a training field, near the demilitarized zone, separating the two Koreas in Pocheon, South Korea April 21, 2017.
She was guarded about the possibility of him making a trip to North Korea as well.
Mattis said the US continues to support the coalition led by Saudi Arabia that's fighting Houthi rebels in Yemen. "South Korea agreement concerning the postponement of joint drills, and there has been no other agreement", South Korea's foreign ministry said in a statement on Wednesday.
US President Trump has pointed the accusatory finger at China while speaking on US-North Korea relations on Wednesday.
Senior U.S. officials expressed irritation that Japan was not forthright about the meeting, despite Washington's near-constant updates to Tokyo on its dealings with North Korea, it said.
Cronin said the reason sequencing matters to the administration is that "without the significant meaningful steps of denuclearization the United States does not support a peacemaking process that is one-sided and that is favorable to North Korea".
Mattis said he was working in coordination with Secretary of State Michael Pompeo's diplomatic efforts - "it's all riding on Secretary Pompeo's shoulders", he said - but he also signaled that smaller-scale exercises are going ahead.
The statement added that Mr Trump can restart the games at any time and that "if he does, they will be far bigger than ever before". The traditional USA calendar for other major drills does not pick up again until next spring, officials say, which could give diplomats and military planners time.