The letter comes just days after thousands of South Koreans flocked to the streets of Seoul to demand peace with North Korea and protest the visit by US President Donald Trump, who previously promised to unleash "fire and fury" against the "rocket man", Kim Jong-un.
Trump is now in Vietnam attending the Asia-Pacific Economic Cooperation summit, but he took the time to tweet: "Why would Kim Jong-un insult me by calling me 'old, ' when I would NEVER call him 'short and fat?'".
"Why would Kim Jong-un insult me by calling me 'old, ' when I would NEVER call him 'short and fat?' Oh well, I try so hard to be his friend - and maybe someday that will happen!"
In the meantime, the 25 million inhabitants of the South Korean capital, Seoul would be in grave danger from the enemy to the north and that United States and allied forces would be "subject to attack by conventional or chemical weapons" which would further delay their entry into the war.
Trump has been working to rally global pressure against North Korea's nuclear weapons program on a trip to Asia.
Asked at a news conference in Vietnam if he could see himself being friends with Kim, the Trump replied: "That might be a unusual thing to happen, but it's a possibility".
The Korean Central News Agency referred to Trump on Saturday as a "destroyer" and a "dotard" who "begged for nuclear war".More news: Alibaba Smashes 2016 Sales Records Just Halfway through "Singles Day" 2017
"Every step you take down this dark path increases the peril you face".
"Odd things happen in life", Trump said.
The post came in response to the country's foreign ministry calling Trump "an old lunatic" over his speech in South Korea. "If it did happen, it would be a good thing for North Korea, and a good thing for lots of other places and good for the world".
Speaking later in Vietnam's capital, Hanoi, Trump said "it would be very, very nice" if he and Kim became friends.
Trump followed up his weird tweet by telling reporters that it would be a "good thing" for him and dictator to become friends.
Trump is in Vietnam as part of a almost two-week tour of Asia, and North Korea's nuclear weapons program has been a major talking point with his Japanese, South Korean and Chinese counterparts.
This is the first time three carrier strike groups will operate together since 2007 during an exercise off the coast of Guam, according to the Navy.