Trump offered a light moment toward the beginning of the talks, joking that they should all get togethher for a photo to look "handsome" and "thin".
The State Department is declining to release any additional information about the calls.
Even Trump admitted this during a visit to Seoul six months ago, when he referred to life in the North as "a hell that no person deserves".
About 28,500 US troops are now stationed in South Korea as a legacy of the 1950-53 Korean War. This year, the springtime war games were conducted in April, delayed due to South Korea hosting the Winter Olympics.More news: Melania Trump Makes Her First Public Appearance in Several Weeks
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With a handshake that lasted for about 13 seconds, North Korea's Kim Jong-un and US President Donald Trump on Tuesday scripted history during the first-ever and much-awaited meeting between the two countries.
Trump's comments Tuesday were a far cry from his speech to the U.N.in September.
Former Vice President Joe Biden has issued a statement blasting President Donald Trump's Singapore summit with North Korean dictator Kim Jong Un, charging he gave Kim "many sought-after wins up front without getting anything in return".
At his post-summit news conference Trump told reporters that the people in Kim's prison camps were the "great winners" today. North Korea is seeking a security guarantee - possibly including a peace treaty formally ending the Korean War - and the removal of the U.S.'s nuclear umbrella protecting allies South Korea and Japan. US President Donald Trump arrived at the venue just 60 seconds before the summit was to begin.
"We may be able to recoup a little bit of that, but I think it is a cost that we're willing to pay and it's our contribution to an worldwide endeavor, which is in our profound interests", he added. The United States and the DPRK commit to hold follow-up negotiations, led by US Secretary Of State Mike Pompeo and a relevant high-level DPRK official at the earliest possible date to implement the outcomes of the US-DPRK summit. "What does it mean to stop war games?" said Ambassador Joseph Yun, who served as the USA special envoy on North Korea at the end of the Obama administration and during President Trump's initial months in office.