In tweets, Trump said everyone "can now feel much safer than the day I took office" and people could "sleep well tonight!"
"President Trump committed to provide security guarantees to the DPRK and Chairman Kim Jong Un reaffirmed his firm and unwavering commitment to complete denuclearization of the Korean Peninsula", said the statement.
Bishop made it clear that agreement between Trump and the North Korean dictator had to involve "complete, verifiable, irreversible" denuclearisation.
The KCNA report - which was also carried by the Rodong Sinmun, official newspaper of the ruling Workers' Party - also claimed that the president pledged to suspend military drills with South Korea, and lift sanctions on the North.
Albright advised that the Trump administration and the U.N. Security Council should not remove sanctions against North Korea early, saying they are the "leverage" in compelling the country to take concrete measures toward denuclearization.
A joint statement issued after the first-ever U.S.
"Before taking office people were assuming that we were going to War with North Korea", Trump tweeted.
Guterres also praised China's key role in resolving the Korean Peninsula issue in April after Kim's visit to Beijing at the end of March.
Japanese Delegation Arrives in Singapore Ahead of Trump-Kim Summit
Kim met the Singaporean prime minister , Lee Hsien Loong, briefly on Sunday, smiling broadly as the two posed for photographs. Trump canceled the summit last month after both sides exchanged criticism but then revived the summit after tensions cooled.
US Secretary of State Mike Pompeo, who is to lead the US side in talks with North Korea to implement outcomes of the summit, arrived in South Korea on Wednesday, to be greeted by General Vincent Brooks, the top US commander in South Korea, and US Charge d'Affaires Marc Knapper.
In addition, he predicts that if the talks do go well, the Korean Peninsula could be reunified.
Echoing that stance, Akira Kawasaki of the ICAN anti-nuclear group said the summit was "a great photo-op", but that "the substance needs to be followed up".
Christopher Hill, chief USA negotiator with North Korea in the George W. Bush administration, suggested in an interview that it's "a little premature" for Trump to say Kim is someone the US can trust.
Following the summit, Trump said verification processes had been discussed during his meeting with Kim, and that Kim understood it would involve accepting large numbers of USA and global personnel into the reclusive country.
Pompeo, after landing in South Korea, met for almost an hour with Gen. Vincent Brooks, commander of U.S. Forces Korea.
KCNA also asserted Trump had "expressed his intention" to lift sanctions against the North - something the USA president had said would happen "when we are sure that the nukes are no longer a factor".
Sen. Bob Corker (R-Tenn.) said Tuesday that he wants Secretary of State Mike Pompeo to brief senators on the substance of what the two nations discussed, including whether US troops stationed on the Korean Peninsula would remain.
The round of diplomacy came as there appeared to be confusion over whether USA sanctions on North Korea would be lifted.