SEOUL (Reuters) -South Korean President Lee Jae Myung is leaning on promises to "Make America Shipbuilding Great Again" during his first official U.S. trip, as the two allies wrangle over other details of their trade and security agreements.

Lee met with U.S. President Donald Trump for their first summit on Monday, and on Tuesday will visit a shipyard owned by South Korea's Hanwha Group to highlight investment plans.

Under a South Korean pledge to inject $350 billion into U.S. projects, shipbuilding has emerged as one of the most concrete areas of investment, with $150 billion earmarked for the sector.

Trump says he wants to revitalise shipbuilding to keep up with China, the world's biggest shipbuilder and operator of the world's largest maritime fighting force.

The potential - and pitfalls - of that project will be on display when Lee visits Hanwha's Philly Shipyard in Philadelphia, one of the largest U.S. shipyards.

Hanwha, which acquired the facility last year, plans to spend as much as $5 billion to take its output from less than two vessels a year to as many as 20, Lee's office said. In comparison, Hanwha Ocean's shipyard in South Korea is 10 times bigger and builds a vessel a week.

"The K-shipbuilding industry, equipped with the world's strongest capabilities, will bring about a renaissance of the U.S. shipbuilding industry and create a new historic turning point for mutual prosperity," Lee said an event at Washington's Center for Strategic and International Studies after the summit.

South Korea's industry ministry said 11 non-binding agreements were signed between U.S. and South Korean companies during Lee's visit, in shipbuilding, nuclear energy, aerospace, gas and critical minerals. In shipbuilding, HD Hyundai agreed with state-run Korea Development Bank and Cerberus Capital to create a multibillion-dollar joint investment fund aimed at strengthening the maritime capabilities of the U.S. and its allies, including shipbuilding, marine logistics infrastructure, and advanced marine technology. Samsung Heavy Industries agreed with Vigor Marine Group to partner in fields such as maintenance and repair of U.S. Navy vessels, shipyard modernisation and joint ship construction.

LEGAL, MANUFACTURING HURDLES

During tariff talks in July, South Korea offered a package dubbed "Make America Shipbuilding Great Again" partly to help modernise U.S. shipyards, which officials in Seoul touted as instrumental in reaching their unwritten trade deal.

U.S. shipyards, which had the world's highest production capacity during World War II, saw their market share fall to 0.04% by 2024. China and South Korea are responsible for 83% of global commercial shipbuilding, according to UN Trade and Development data.

"We're going to go back into the shipbuilding business again," Trump said during his Oval Office meeting with Lee.

Experts, industry sources and South Korean officials say there will be a lot of work required to get there.

"I think the U.S. shipbuilding industry hasn't had to compete very much. Facilities are old, and there's a shortage of technicians," Steve SK Jeong, head of the Naval Ship Global Business at Hanwha Ocean, previously told Reuters.

Training local workers could take four to five years, and it is hard to find people willing to do difficult shipyard work, South Korean industry sources told Reuters.

Jeong said Hanwha is working to modernise facilities, train and equip workers, and transplant its manufacturing process that can build ships much faster.

Hanwha has said it plans to make arrangements to use idle docks owned by others near the Philly Shipyard to expand construction capacity, as well as improve project management and use automation such as welding machines to speed up production.

Issues obtaining parts like steel plates may also hinder rapid progress.

Trump said some U.S. ships would still be built in South Korea for now.

"We're going to be buying ships from South Korea," he said. "But we're also going to have them make ships here with our people."

South Korean officials said that unless some U.S. protectionist policies are eased, construction of full ships or modules to be delivered to U.S. shipyards may be limited.

The 1920 Jones Act requires goods moved between U.S. ports to be carried by ships built domestically.

Similarly, the Byrnes-Tollefson Amendment prohibits the construction of U.S. Navy vessels in foreign shipyards, although the president retains the authority to waive its provisions for national security. Some U.S. lawmakers have proposed changes that would open the door for U.S. allies to participate more.

Wi Sung-lac, Lee's national security adviser, acknowledged the legal restrictions.

"We're conducting various studies to increase cooperation while taking into account various detours and institutional improvements," he said.

(Reporting by Joyce Lee; Additional reporting by Heejin Kim and Ju-min Park; Writing by Josh Smith; Editing by Lincoln Feast.)