The South, which is technically still at war with nuclear-armed North Korea, said it expects to launch its first nuclear-powered submarine by the mid-to-late 2030s, using its own technology.
AFP takes a look at what we know:
What is the deal?
Trump said last week he had approved ally South Korea's plan to build a nuclear-powered submarine after meeting counterpart Lee Jae Myung on the sidelines of an APEC summit.
Lee's office has said Seoul needed US approval because of the requirement for nuclear fuel, which is restricted for military use.
The exact scale and cost of the submarine project are unknown but South Korea has said it will invest $150 billion in enhancing the US shipbuilding industry.
From there, the details start to become murky.
South Korea's promised investment is part of a response to the tariff blitz Trump launched after his return to the White House in January and was announced before the submarine approval.
Critics argue that, given remarks that Trump made on his Truth Social platform, Washington could have pushed Seoul to invest in a shipyard in Philadelphia in exchange for US support to build the vessel.
The two sides now appear to be hammering out the details.
Where will it be built?
Trump said last week that South Korea would build the submarine in Philadelphia. US nuclear technology is among its most sensitive and tightly guarded military secrets.
He also mentioned a shipyard run by a South Korean company, although Seoul later said that did not align with its plans.
Some think the idea could still work to South Korea's advantage.
"The shipyard, acquired by South Korea's Hanwha Group, has extensive experience with the US Navy and would offer valuable access to American design and operational know-how," Choi Il, head of The Submarine Research Institute, told AFP.
However, South Korea's presidential office said on Friday that Seoul will develop and build the vessel at home, with US-supplied fuel, and that the discussion between Trump and Lee was based on that "premise".
South Korean Defence Minister Ahn Gyu-back said the US yard is "currently lacking sufficient technology, workforce, and facilities". National security adviser Wi Sung-lac said it "wouldn't be realistic to invest in submarine facilities" there.
Hanwha Ocean has run the Philadelphia shipyard since last year.
How is the submarine different?
Nuclear-powered submarines can remain submerged for months, unlike their diesel-powered predecessors that must surface regularly to recharge their batteries.
"Submarines are designed for stealth infiltration, but those with shorter submergence times must surface more often, increasing the risk of detection," Hong Sung-pyo, senior researcher at the Korea Institute for Military Affairs, told AFP.
"To conduct challenging or high-level missions, a country needs advanced intelligence and precision strike capabilities, and nuclear-powered submarines are one of the most effective tools in that regard."
South Korea and the United States are moving to transfer wartime operational control of their combined forces to a South Korean commander with a US deputy, and experts say the submarine will strengthen Seoul's push for greater military autonomy.
Currently, Washington would command allied troops in the event of war on the Korean peninsula.
Why does South Korea want it?
South Korea is protected by the US nuclear umbrella and there are nearly 30,000 US troops stationed there.
Analysts say developing a nuclear-powered submarine would mark a significant leap in South Korea's naval and defence industrial base, allowing it to join a select group of countries with such vessels.
Only the United States, China, Russia, India, France and Britain currently have them.
North Korea has bolstered its military ties with Russia and has repeatedly declared itself an "irreversible" nuclear power.
The "possibility of sudden attacks from the East Sea will be a source of anxiety" for Pyongyang, said Ahn Chan-il, a defector-turned-researcher who runs the World Institute for North Korea Studies.
"Feeling threatened by this plan backed by Washington, Pyongyang is likely to respond aggressively -- and another nuclear test cannot be ruled out," Ahn told AFP.
And the final details?
Seoul's Policy Chief Kim Yong-beom said last week the two sides have nearly "finalised the details of the agreement", and that a factsheet "combining (tariff and) security matters" would be released.
South Korea has yet to announce a detailed deal on tariffs and its investment pledge, which totals $350 billion and includes the shipbuilding pledge, that was agreed in exchange for the cut in US tariffs to 15 percent.
Defence Minister Ahn told a parliamentary hearing this week "the process appears to have been delayed as various issues, including nuclear-powered submarines" were worked out.
The Presidential office in Seoul said on Friday a final document could be released "anytime" if "things go smoothly".
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