The US leader, standing alongside his South Korean counterpart Moon Jae-In, reiterated he was prepared to use the full range of American military might to halt Pyongyang's march towards becoming a full-fledged nuclear power.
But he added: "It makes sense for North Korea to come to the table to make a deal that is good for the people of North Korea and the people of the world."
Trump's tone in Seoul, whose 10 million inhabitants would find themselves on the front line of any conflict, was in marked contrast to previous rhetoric.
Trump has traded personal insults and threats of war with North Korean leader Kim Jong-Un, raising fears of possible US military action and rapid escalation.
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But in the South Korean capital, just 35 miles south of the Demilitarised Zone that divides the peninsula, the US president was reassuring.
"Ultimately, it will all work out," he said. "It always works out. It has to work out."
Chinese President Xi Jinping -- whom he has often described as holding the key to disarming the North -- has been "very, very helpful", he said, expressing hopes Russia would be similarly co-operative.
Trump goes on China tomorrow after addressing the South Korean parliament.
"We are going to have an exciting day tomorrow for many reasons that people will find out," he said at a state dinner tonight, without elaborating.
Trump arrived from Japan, where he secured Tokyo's full support for Washington's stance that "all options are on the table" regarding Pyongyang, and declared its nuclear ambitions "a threat to the civilised world and international peace and stability".
After a relaxed few days in Tokyo, Seoul is a more complicated stop for the mercurial US president.
Trump's relationship with the liberal-leaning Moon has been cool, and the former real estate magnate has railed at South Korean moves to engage its neighbour -- something he has previously labelled "appeasement".
But he described Moon as a "fine gentleman" in a tweet early today.
"The partnership between our two nations and our two people is deep and enduring," Trump added at the dinner.
"They say one knows a true friend when one is in need," he told Trump. "The United States is a true friend who has been with us and has bled with us in our time of need."
South Korea is rolling out the red carpet for Trump as it seeks assurances about the alliance and US resolve.
But while Trump has threatened Pyongyang with "fire and fury", Moon is mindful that much of Seoul is within range of the North's artillery and in an address to parliament last week demanded: "There should be no military action on the peninsula without our prior consent."
Kim Hyun-Wook, a professor at the Korea National Diplomatic Academy, told AFP the two allies have "subtle differences in their positions" and underlying suspicions about each other.
North Korea itself welcomed Trump to the region with a rhetorical volley via the ruling party newspaper Rodong Sinmun, calling the US a "thrice-cursed nuclear criminal" and condemning "Trump's mad remarks".
Commerce was also on Trump's agenda in Seoul, and he demanded a "free, fair, and reciprocal" trade deal with his security ally, calling their existing agreement "quite unsuccessful and not very good for the United States".
His administration has caused consternation in Seoul by demanding the renegotiation of the five-year-old US-Korea free trade agreement, which Trump has called a "horrible deal" and a "job killer".
Some observers have fretted that a gaffe by a president given to off-the-cuff remarks could send tensions rising on the peninsula.
"If Trump says anything that can provoke North Korea, it could send military tensions soaring again," said professor Koo Kab-Woo from the University of North Korean Studies in Seoul.
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