The two leaders were scheduled to meet one-on-one before an expanded working lunch with aides.
Earlier, North Korean state media confirmed that Kim Jong Un will discuss denuclearisation with Mr Trump at their Singapore summit.
KCNA said the pair would discuss a permanent and durable peace-keeping mechanism on the Korean Peninsula and other issues of mutual concern.
The report also said Mr Kim was accompanied by his foreign minister Ri Yong Ho, defence minister No Kwang Chol and his sister Kim Yo Jong.
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Both parties have arrived in Singapore ahead of a historic coming together of Washington and Pyongyang.
The talks will be the first between a US and North Korean leader and will mark a sharp turnaround in the status of Mr Kim from international pariah to global player.
Just a few months ago, he and Mr Trump had been at loggerheads – trading insults and threats over Pyongyang’s nuclear missile programme.
Asked by a reporter how he was feeling about the summit after touching down, Mr Trump said Very good.
Mr Trump arrived aboard Air Force One just a few hours after Mr Kim, who has only publicly left his country three times since taking power in 2011.
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His visit to Singapore is his longest trip overseas as head of state.
Mr Kim met Singapore’s PM shortly after landing and said Singapore’s role would be recorded in history if the summit is a success.
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Mr Trump has said he will know within a minute if the North Korean leader is serious and soon after his arrival in Singapore, he wrote on Twitter Great to be in Singapore, excitement in the air!
The White House has claimed credit for bringing Mr Kim to the table through a concerted campaign of tough economic sanctions, diplomatic efforts and the threat of military action.
Analysts believe Mr Kim’s engagement is aimed at getting the US to ease crippling sanctions that have squeezed his poverty-stricken country.
He will also see a victory in having secured recognition and a seat at the negotiating table with the head of the world’s leading superpower.
The on-off nature of the meeting means Singapore, which was chosen due to its history of holding high-profile summits and because it is seen as a secure location, has had just two full weeks to prepare.
The US president flew there from a fractious G7 summit, which he threw into disarray after leaving by pulling out of an agreed communique and accusing Canadian prime minister Justin Trudeau of being dishonest and weak.
News Source SkyNews