Trump announced that US would halt military exercises in South Korea, something widely seen as a concession as Pyongyang has long claimed they are invasion rehearsals.
The president, however, said the sanctions on North Korea for its nuclear tests will remain for now.
North Korean leader Kim Jong Un on Tuesday pledged to work toward the ‘complete denuclearisation’ in return for security guarantees from the United States as Donald Trump wrapped up his historic summit with outcomes that could ease tensions and reshape the geopolitics of the Asia-Pacific region.
"Yesterday's conflict does not have to be tomorrow’s war," Trump said following more than four hours of intense talks with Kim, which he described as ‘honest, direct and productive’.
Trump said Kim 'reaffirmed' his commitment to denuclearisation of the Korean Peninsula and also agreed to destroy a missile engine test site.
"We are ready to write a new chapter between our nations," Trump told reporters after the much talked about summit -- the first between a sitting US president and North Korea's top leader.
He also announced that he would halt US military exercises in South Korea, something widely seen as a concession as Pyongyang has long claimed they are invasion rehearsals.
The president, however, said the sanctions on North Korea for its nuclear tests will remain for now.
Trump and Kim conducted a comprehensive, in-depth, and sincere exchange of opinions on the issues related to the establishment of new relations between the two countries and the building of a lasting and robust peace regime on the Korean Peninsula, according to a joint statement signed by Trump and Kim.
‘President Trump committed to provide security guarantees to the DPRK (Democratic People's Republic of Korea), and Chairman Kim Jong Un reaffirmed his firm and unwavering commitment to complete denuclearisation of the Korean Peninsula,’ the statement said.
It said the two sides committed to recovering POW/MIA (prisoners of war and missing in action) remains including the immediate repatriation of those already identified.
The document was signed after the two leaders had a one-on-one meeting, with translators only, followed by an expanded meeting including their top aides and a working lunch at Capella Singapore hotel in Sentosa Island after months of diplomatic twists and turns.
"We signed a joint statement that is an unwavering commitment to complete denuclearisation of North Korea," Trump said.
WATCH: Trump and Kim share historic handshake
He said the US is ‘prepared to start a new history’ with North Korea.
"Kim told me that North Korea has already destroyed a major missile engine testing site," he said, without elaborating on it.
In response to a question about denuclearisation, Trump said, "We're starting that process... very quickly."
Trump said there will be a meeting next week to go over the details of the denuclearisation process.
"We are working with the regional countries on getting this deal going. We are sitting with (National Security Advisor) John Bolton next week to go over the details, to get this stuff done. We are working with South Korea, Japan, China to a lesser extent," he said, while addressing an hour-long press conference.
When asked about North Korea's future economic model, Trump said it is for the country and its people to decide. He pointed out the real estate potential of its ‘great beaches’ which can be seen on missile test footage.
Earlier, Trump said the summit went 'better than anybody could have expected'.
"We have decided to leave the past behind," Kim said through a translator, after signing the statement.
"The world will see a major change," he added.
Trump said he was very proud of what took place today and the two leaders would ‘take care of a very dangerous problem for the world’.
The 71-year-old Trump said he has developed a ‘very special bond’ with 34-year-old Kim.
Trump said Kim is ‘a very talented man’ and he will invite him to the White House at the ‘appropriate time’, and he will also travel to Pyongyang at a certain time.
Earlier on Tuesday morning, the summit began with the two leaders arriving separately at the luxurious hotel.
They walked towards each other, stood face to face for the first time and shared a 12-second handshake against a backdrop of American and North Korean flags.
They then appeared to share a few light-hearted words as they walked down a corridor to the hotel's library.
The two leaders held one-on-one meeting for around 45-minutes with just translators present.
According to North Korean media, Kim actually arrived at the venue seven minutes earlier than Trump to show respect as it's cultural, the young one should arrive earlier than the elder one.
The red tie that Trump wears may also show some respect to Kim as well, it's the colour that North Koreans like.
Later, they held delegation-level talks. Kim was asked at least three times if he would give up his nuclear weapons. In response, he just smiled.
"There will be challenges ahead but we will work with Trump. We overcame all kinds of skepticism and speculation about this summit and I believe that this is good for the peace," Kim said.
After the delegation-level meeting, Trump joined Kim for a working lunch which had a mix of Western and Asian dishes, such as Korean stuffed cucumber and beef short rib confit with some Haagen-Dazs ice cream to top things off.
The two leaders then took a post-lunch stroll in the courtyard of the hotel.
On the eve of the summit at Sentosa, the US had offered 'unique' security guarantees to North Korea in return for a ‘complete, verifiable and irreversible’ denuclearisation.
US President Donald Trump joined North Korean leader Kim Jong Un for a working lunch which had a mix of Western and Asian dishes, such as Korean stuffed cucumber and beef short rib confit with some Haagen-Dazs ice cream to top things off.
After their bilateral meeting at the Capella hotel in Singapore's Sentosa island, Trump and Kim met for a working lunch along with their aides.
As the two men entered the room, photographs were taken, with Trump joking about wanting to get a "beautiful picture" in which he looked good.
The two leaders and their respective delegation were seated on either side of a long white table facing one another. The table was decorated with green and white flowers.
The full menu includes:
Starters: Prawn cocktail with avocado salad, green mango kerabu or "oiseon," a Korean stuffed cucumber.
Main course: Beef short rib confit, Sweet and sour crispy pork with Yangzhou Fried Rice or "Daegu jorim," a Korean soy braised cod fish
Desserts: Dark chocolate tartlet ganache, Vanilla ice cream or "Tropezienne," a pastry dessert.
