The announcement follows a diplomatic breakthrough that re-established communications
between North and South Korea, though US officials took a skeptical stance Thursday about Kim's sincerity in soothing tensions.
In a phone call on Thursday, Trump and Moon "agreed not to host joint military drills during the period of Pyeongchang Olympics," in South Korea, the Blue House in Seoul said in a statement. The Games are scheduled for February 9 to 25.
A senior US military official also confirmed to CNN that there would be no joint exercises during the Games.
North Korean leader Kim Jong Un has long bemoaned the joint US-South Korean drills and has often called them a direct threat to Pyongyang.
On Wednesday, Kim gave the order to revive a hotline with South Korea that had sat dormant for almost two years, in a U-turn following a year of tensions and hostility with the US, as well as neighbors with South Korea and Japan. Contact between Pyongyang and Seoul was made on the hotline Wednesday and Thursday.
That breakthrough came after Kim expressed hope in his New Year's Day address that his country might participate in the Olympics.
"America supports President Moon 100%," Trump said to Moon during the 30-minute phone call, according to the Blue House statement.
Trump also told Moon that he would send high-level representatives to the Winter Games, including his own family.
The White House did not immediately reply to CNN's request for comment.
The decision to hold off on military drills is a cooler response from the US President, who bragged in a tweet that his nuclear button was "much bigger & more powerful
" than Kim's.
Trump also sought to take credit for the resumption of communications between Pyongyang and Seoul on Thursday.
"With all of the failed 'experts' weighing in, does anybody really believe that talks and dialogue would be going on between North and South Korea right now if I wasn't firm, strong and willing to commit our total 'might' against the North," Trump tweeted Thursday morning.
"Fools, but talks are a good thing!" he added.
Moon hopes to 'set mood' for denuclearization talks
Moon and Trump also spoke about the denuclearization of the Korean Peninsula.
North Korea ratcheted up its missile testing last year, and in September it carried out its most powerful of its six nuclear tests, prompting fresh sanctions on the country.
Kim's comments on possibly sending athletes to the Winter Games and the resumption of communications with South Korea have given hope that Pyongyang may be more open to dialogue on its nuclear ambitions than it suggested last year.
Moon said that the resumption of communications between the two Koreas was certain to "help to set the mood for a conversation between the US and North Korea to resolve nuclear issues."
US military skeptical of Kim outreach
But Kim's overtures to South Korea are being looked up with skepticism by US intelligence and military officials for now. Several officials tell CNN that the US wants to see a consistent pattern of positive behavior by North Korea before concluding that the North Korean leader is truly extending an olive branch to South Korea.
Officials believe there is an impact on North Korea from sanctions that is resulting is shortages of key items like fuel.
But, so far, they are not concluding that the impact of sanctions has directly motivated Kim's overtures to the South. US officials are also looking at reports the impact of sanctions has hit some of North Korea's elites who surround Kim, making him concerned about the viability of his rule and his family.
But officials stress that given the secrecy surrounding the regime, they cannot be certain about the validity of the reports. Also, there is no indication that funding shortages are hitting Kim's missile and nuclear program, one official emphasized.