Trump, who a year ago lambasted his chief diplomat for talking about negotiations with the nuclear-armed North, told reporters at Camp David that some dialogue or direct conversation with Kim Jong Un was not beyond the realm of possibility.
South Korean President Moon Jae-in, who has long advocated for an ongoing dialogue with North Korea, quickly reacted to Kim's speech by saying it was "a response to our proposal to turn the Pyeongchang Olympic Games into an epoch-making opportunity to improve inter-Korean relations and establish peace".
The exercises have been a major source of tension because North Korea considers them an invasion rehearsal, although South Korea and the United States have repeatedly said the drills are defensive in nature.
"If North Korea is serious about denuclearization talks, they should accept (the decision to delay the exercise) as meeting one of the conditions for talks and refrain from asking for complete suspension of joint military drills". "We'll see if the North Koreans come with more than just wanting to talk about the Olympics".
The remarks came shortly after North Korea agreed to hold an inter-Korean dialogue on Tuesday to discuss sending its delegation to the PyeongChang Games, which will be held from February 9-25.
Trump had earlier called the proposed inter-Korean talks a "good thing" and that he would send a high-level delegation, including members of his family, to the Winter Olympics, according to South Korea's presidential office.
US President Donald Trump has said that he was willing to speak to North Korean' Kim Jong-un.
Trump added: "If something can happen and something can come out of those talks, that would be a great thing for all of humanity".
They may not mix, but that doesn't stop them from being frequently tossed into a blender anyway. "We're very firm", Trump said.
The ramped-up momentum for inter-Korean dialogue follows a year of missile and nuclear tests by North Korea as well as an exchange of bellicose comments from Trump and Kim, which raised alarm across the world.
North and South Korea are holding their first official talks on Tuesday following the reopening of a phone line between the two countries this week.
While it is certainly true that North Korea has been a frustrating negotiating partner in the past, and that its nuclear weapons program continues to move forward despite years of diplomacy, those are not persuasive arguments against further efforts to engage.