By Jessie Yeung, Gawon Bae, Mitchell McCluskey, CNN

(CNN) — President Donald Trump is willing to meet with North Korean leader Kim Jong Un, he told his South Korean counterpart during a meeting on Monday, where they discussed peace in the Korean Peninsula and Pyongyang’s nuclear weapon capabilities.

South Korean President Lee Jae Myung, who was elected in June, asked Trump to help establish peace between the two Koreas during his visit to the White House – claiming the situation had been more stable during Trump’s first term in office.

“I think you are the first president to have so much interest in the world’s peace issues and actually made achievements,” Lee said. “So, I hope you would make peace on the Korean Peninsula … and meet with Kim Jong Un.”

He added that he would “actively support” Trump if he wanted to “play the peacemaker,” and that the US president was “the only person who can actually solve” tensions between North and South Korea, who remain technically at war after the Korean War ended in 1953 with an armistice, not a peace treaty.

Lee’s meeting was a major test for South Korea’s new leader at a time when both Seoul’s trade and military relationships with the US are facing pressure from Trump’s “America First” policies.

Lee, who took office in June after his predecessor and conservative political rival was impeached, travelled with a bevy of CEOs and business leaders from some of South Korea’s top firms who announced a slew of investments during the trip.

Korean Air said it intends to purchase 103 aircraft from Boeing, along with engines and a maintenance program from GE Aerospace and CFM International, totaling $50 billion, according to a statement.

Meanwhile, Hyundai Motor Group said it would increase its investment in the United States from a previously planned $21 billion to $26 billion in a Tuesday statement.

In total South Korean businesses are expected to invest a total of $150 billion in the US, Lee announced during a South Korea-US business round table that he attended after the summit.

Golf clubs and cowboy hats

Among the bespoke gifts Lee handed Trump were two cowboy hats embroidered with Trump’s “Make America Great Again” campaign slogan, a tailor-made golf putter, and a “turtle ship” model.

And in a nod to Trump’s love of golf and various golf properties, Lee joked that a Trump Tower should be built in North Korea, “so I can go play golf in Pyongyang as well.”

Trump – whose peacemaking efforts and negotiations with both South and North Korea had been a key part of his tumultuous first term – quickly agreed.

“I will do that, and we’ll have talks. He’d like to meet with me,” Trump said of Kim. “We look forward to meeting with him, and we’ll make relations better. You’ll help that.”

It’s hard to say whether such a meeting might go ahead. North Korean state media claimed that joint military drills between the US and South Korea showed Washington’s intention to “occupy” the Korean peninsula, Reuters reported Tuesday morning local time in South Korea.

Earlier this and last year, Kim and his powerful sister Kim Yo Jong had stepped up their rhetoric, vowing to maintain North Korea’s nuclear arsenal and to destroy South Korea with nuclear weapons if Pyongyang is attacked.

North Korea is now able to produce 10 to 20 nuclear weapons per year as the country has expanded its capabilities, Lee said on Monday after his meeting with Trump, without providing evidence.

That figure is “higher than normally assumed so (it) probably implies additional uranium enrichment capacity” in North Korea, said Hans Kristensen, director of the Nuclear Information Project at the Federation of American Scientists.

On Saturday, just two days before the summit between Trump and Lee, North Korea test launched two new air defense missiles, according to state media KCNA. And Kim – and potentially his arsenal – are now bolstered by burgeoning ties with Moscow, with North Korean troops sent to fight for Russia in its war against Ukraine.

Previous Trump meetings with Kim

It wouldn’t be the first time Trump met Kim – someonehe boasts of having a “very good relationship” with. “He was very good with me … We got along great,” he said on Monday, claiming to know Kim “better than anybody, almost.”

It wasn’t always this way. There was a period of serious tensions in 2017, when North Korea escalated its provocations with missile tests – and Trump responded with tweets taunting Kim as “Little Rocket Man” and threatening to respond with “with fire and fury like the world has never seen.”

But those tensions cooled as the two became pen pals, exchanging what Trump has described as “love letters” that ultimately led to a series of unprecedented meetings between the two leaders in 2018 and 2019.

During one meeting in the demilitarized zone (DMZ) between North and South Korea, in a remarkable moment, Kim invited Trump to step over the border into North Korea – making him the first sitting US president to enter the highly isolated autocratic nation.

But the talks ended without any breakthrough, wrapping up abruptly in Hanoi in 2019 – and efforts at denuclearization or peace negotiations fizzled out afterward.

Pyongyang has since refused to reengage with the US, experts say, and restarted weapons testing it had appeared to pause alongside that dialogue. While it has yet to initiate a nuclear test since 2017, Kim has since vowed to increase the country’s number of nuclear weapons “exponentially.”

Speaking at an event hosted by Washington-based think tank Center for Strategic and International Studies, South Korea’s Lee warned that the number of North Korea’s nuclear weapons has increased 2.5 times in just the last few years.

The nation is now in the “final stages” of developing intercontinental ballistic missiles (ICBMs) that “can target far away distances,” he said, adding: “The situation is deteriorating.”

And at a congressional hearing earlier this year, Army Gen. Xavier T. Brunson testified that the US expects North Korea to make progress this year in other parts of its weapons program.

“In the coming year, we expect (North Korea) to further develop hypersonic and multiple, independently targetable reentry vehicle capabilities to complete (their government’s) goals,” Brunson said.