Trump, who returned to Washington early on Wednesday, hailed the meeting with Kim - the first between a sitting USA president and a North Korean leader - as a success that had removed the North Korean threat.
"I don't think it would be the end of the world, because it's the world we already live in", he said.
The United States did, however, commit to suspending joint military exercises with South Korea, Trump told reporters before departing the summit site.
However this stock phrase, favored by Pyongyang, stopped short of longstanding United States demands for North Korea to give up its atomic arsenal in a "verifiable" and "irreversible" way.
Kimmel noted that Trump told the press he had formed a "special bond" with Kim after meeting with the North Korean leader for only 38 minutes.
Ambassador Joseph DeTrani, who served as a top USA negotiator with Pyongyang before the last attempt at diplomacy broke down in 2009, was more optimistic.
While Trump claimed a historic breakthrough at the most significant diplomatic event of his presidency, Secretary of State Mike Pompeo, was more measured.
When Baier pointed out some of the unsavory things Jong Un is accused of doing in North Korea, Trump demurred.
The president said there was no tit-for-tat deal with Pyongyang where there is denuclearization on the Korean Peninsula in exchange for an end to USA military exercises with South Korea.
Trump added: "Before taking office people were assuming that we were going to War with North Korea".
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After North Korean dictator Kim Jong Il died in 2011, his son, Jong Un, was named the head of the nation and went on to purge other family members from the party. "President for life. No, he's great", Trump said, referring to Xi.
But ahead of his sit down with Kim, Trump had said he would gauge whether the North Korean leader was honest with "just my touch, my feel".
Recent analysis by Chinese scholars and the Ministry of Foreign Affairs both indicate that Beijing foresees a strengthened role for China as a strategic powerbroker in the Trump-Kim agreement.
Former U.S. ambassador Bill Richardson told VOA he is concerned about no verification of what the North Koreans will do about missile technology in their country, no details of nuclear reduction or the peace treaty ending the Korean War from the early 1950s, and human rights.
Photos of Kim standing side-by-side with Trump on the world stage were splashed across newspapers.
At their historic summit, Kim made few concessions beyond agreeing to "complete denuclearization of the Korean Peninsula" - a term his regime and the USA can't agree on a definition for. The joint statement implicitly links denuclearisation to "new US-DPRK relations" and to mutual confidence building (that) can promote the denuclearisation of the Korean Peninsula.
The traditional USA calendar for other major drills would not pick up again until next spring, officials say.
A key Trump ally, Republican Senator Tom Cotton, appeared to acknowledge the success of North Korea's model in an interview after the summit concluded. The next scheduled major exercise, involving tens of thousands of troops, normally is held in August.
North Korea is believed to possess more than 50 nuclear warheads, with its atomic program spread across more than 100 sites constructed over decades to evade global inspections. He said he planned to continue sharing the view with Washington and Seoul.