Trump also tweeted a defence of widespread criticism of the summit, his apparent concessions to Kim and his praise of the authoritarian leader.
"This week, the South Korean and US defense ministries will jointly announce the results of their discussions", the source added.
With Trump's abrupt about-face, his administration appears to be acquiescing to North Korea's request.
South Korea'sChosun Ilbo newspaper reported that the upcoming Ulchi Freedom Guardian exercise, which usually begins in late August, would be canceled as part of the suspensions.
"There will be a meeting at the Pentagon later this week with the secretary of Defense, secretary of State and the National Security Advisor on this issue".
-South Korean command and control exercise that began in 1976 and is created to enhance readiness, protect the region and maintain stability on the Korean Peninsula. He added that dumping the drills will save the U.S. Last year, about 17,500 USA service members took part, as well as participants from Australia, Canada, Colombia, Denmark, the Netherlands, the United Kingdom and New Zealand.
The summer exercise, Ulchi Freedom Guardian, consisted mainly of computer simulations to hone joint decision-making and planning.
Trump has also said the good chemistry he developed with Kim leads him to believe the dictator is serious about a pledge to denuclearize the Korean Peninsula.
About 28,500 US troops are stationed in South Korea, a legacy of the Korean War, which ended in 1953 in an armistice that left the two Koreas technically still at war. The annual Max Thunder exercise went forward without U.S.
Trump said via Twitter on Sunday that it was his initiative to suspend military drills - a step North Korea has long sought.
After the news broke, Blue House spokesperson Kim Eui-kyeom said that the government is getting enough information about relations between North Korea and China and applauded the nation's intelligence-gathering capabilities. Jack Reed, D-Rhode Island, ranking member of the Senate Armed Services Committee, said in a statement.
Roughly 28,000 U.S. troops are stationed in South Korea as a deterrent measure.
"The South Korean and the U.S. defense ministries would maintain close coordination to make sure there is no daylight in the combined forces' readiness posture", the ministry said.
The Pentagon has typically avoided describing the joint exercises as "war games" and has previously insisted they are not provocative because they are exclusively for defensive purposes. "Plus, I think it's very provocative".
A vehicle believed to be carrying North Korean leader Kim Jung Un enters the Diaoyutai State Guest House in Beijing, China, in this photo taken by Kyodo June 19, 2018.
Sports officials from the rival Koreas met at a border village on Monday to discuss how to cooperate in the Asian Games being held in Indonesia in August.
South Korea made also made clear that it will continue with its own defense readiness exercises during the suspension of the major military exercises with the U.S.
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