As tensions over Pyongyang's weapons programme have soared, the US president has traded personal insults and threats of war with North Korean leader Kim Jong-Un, but the South's capital and its 10 million inhabitants would be on the front line of any conflict.
On Twitter Trump described Moon as "a fine gentleman", adding: "We will figure it all out!"
The tone was in marked contrast to a previous Trump tweet in which he accused Moon -- who has backed engagement with the North to bring it to the negotiating table -- of "appeasement".
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 declaring its nuclear ambitions "a threat to the civilised world and international peace and stability".
He enjoyed three days of near-bromance with Prime Minister Shinzo Abe, calling him "wonderful" after a round of golf and describing US-Japan ties as "really extraordinary".
Trump's relationship with Moon, a former human rights lawyer, is noticeably cooler, stoking concerns about the decades-old alliance and fears in Seoul that it could be sidelined by the US in favour of Tokyo.
But at Camp Humphreys, where US forces stationed in the country have moved their headquarters from downtown Seoul, the two men sought a rapprochement.
"Ultimately, it will all work out" on North Korea, said Trump. "It always works out. It has to work out."
And Moon, whose parents were evacuated from the North on a US ship during the Korean War, was abundant in his praise for the United States.
"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 messages of assurance 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."
In an editorial Tuesday ahead of Trump's arrival, the Korea Times said of the US president: "His 'rhetorical bombs' say it all."
"However calm Koreans are reported to be about the Trump-Kim war of words, we cherish our lives as much as Americans do theirs and feel scared by the outlook of war," it added.
Kim Hyun-Wook, a professor at the Korea National Diplomatic Academy, told AFP that the two allies have "subtle differences in their positions" and underlying suspicions about each other.
President Donald Trump, left, and South Korean President Moon Jae-in, right, have lunch with U.S. and South Korean troops. Source: AAP
'Reckless remarks'
Citizens views are mixed, with both pro and anti-Trump demonstrations taking place in downtown Seoul since the weekend, sometimes only a few blocks apart, and a heavy police presence lined the route of his motorcade Tuesday.
North Korea, which carried out by far its most powerful nuclear test to date in September, 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".
Another issue on his agenda will be commerce between the US and South, with Trump saying he had "a terrific meeting scheduled on trade" with Moon.
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".
"It will start working out and working out so we create lots of jobs in the United States, which is one of the many important reasons I am here," Trump said.
On Wednesday, Trump will speak to South Korean MPs but his visit will not include a trip to the Demilitarised Zone dividing the Korean peninsula, with the administration downplaying the destination as "a little bit of a cliche".
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.
