Washington (CNN) President Donald Trump said Saturday that he looks forward to seeing North Korean's Kim Jong Un "in the not too distant future," but did not give any details about progress toward another meeting between the two leaders.

"In a letter to me sent by Kim Jong Un, he stated, very nicely, that he would like to meet and start negotiations as soon as the joint U.S./South Korea joint exercise are over," the President tweeted.

The message on social media comes after Trump said Friday that he received a "very beautiful" letter from Kim, the North Korean leader who has repeatedly violated UN resolutions in recent weeks with a series of short-range missile tests

Speaking to reporters on the White House South Lawn, Trump described the three-page missive as "very positive," and hinted at some of the contents.

Kim made clear he is not happy with US "tests," Trump said, later clarifying that he meant joint US-South Korea military exercises.

"He's not happy with the testing," Trump said. "It's a very small testing that we did, but he wasn't happy with the testing- he put that in the letter."

Trump went on to downplay Kim's missile tests, which North Korea has said are meant to protest the joint military drills and pose a threat to US allies in the region.

"I say it again," Trump told reporters, "There have been no nuclear tests. The missile tests have all been short-ranged — no ballistic missile test. No long-range missiles."

Trump also claimed on Saturday that Kim's letter was a "small apology" for the short-range missile testing.

"It was a long letter, much of it complaining about the ridiculous and expensive exercises. It was also a small apology for testing the short range missiles, and that this testing would stop when the exercises end," Trump tweeted Saturday.

Trump's comments come after he declared this week that Seoul must pay the US more for help in defending itself against Pyongyang's potential aggression — highlighting the contrast in his treatment of the two Koreas.

with little more than a shrug. Instead, he appears to be turning his frustrations about the peninsula on South Korea. Trump has reacted to five North Korean missile tests in about two weekswith little more than a shrug. Instead, he appears to be turning his frustrations about the peninsula on South Korea.

Trump chided Seoul on Twitter Wednesday for paying "virtually nothing" for US protection, while two administration officials said that behind closed doors, the President is fuming that South Korea is not doing more to contain Pyongyang's increased aggression.

Speaking to reporters Wednesday on the White House South Lawn, Trump said the US and South Korea "have made a deal" in which Seoul will "pay a lot more money" toward the costs of basing US military personnel in the country -- the second increase the Trump administration has pushed for and gotten this year.

'Virtually nothing'

"We've been helping them for about 82 years and we get nothing, we get virtually nothing," Trump said, incorrectly, and hinted that he would push for still higher payments in future. "They've agreed to pay a lot more and they will agree to pay a lot more than that."

Two US officials said that Trump has further soured on South Korea in recent months. As North Korea has grown more aggressive with its missile launches, the President sees it as South Korea's role to rein in Pyongyang and does not think Seoul has done much to deliver. NSC officials declined to comment on those assertions.

Trump's dismissal of Pyongyang's missile tests, his push to ratchet up South Korea's payments to stay under the US security umbrella and his criticism of Seoul raise concerns that North Korea is successfully driving a wedge between Washington and Seoul, analysts said.

On Friday, Trump hinted he might arrange another bonding opportunity with the North Korean leader, telling reporters that, "I think we'll have another meeting."

At the same time, Trump's transactional approach to South Korea prompts questions about whether he is committed to an alliance that serves US interests as much as it does Seoul's.

"The US-South Korean alliance was forged in blood during the crucible of the Korean War," said Bruce Klingner, a senior research fellow at the Heritage Foundation. "Its enduring motto is katchi kapshida -- 'we go together' -- not 'we go together, if we are paid enough.'"

Klingner and others said the US defense of its national interests in Asia requires US bases, access, enough deployed military forces to deter aggression, robust follow-on forces and strong alliances with South Korea and other Asian partners.

Kim has been focused on undermining the US-ROK alliance in particular, said David Maxwell, a senior fellow at Foundation for Defense of Democracies. One of Kim's "main line of efforts is to divide and conquer the US-ROK alliance," Maxwell said.

Vipin Narang, a political science professor at MIT, called Trump's assessment of the alliance "a stark break from 70 years" of US presidential custom.

"2019 is weird," Narang said. "The President has more respect for Kim Jong Un than he does for South Korea ... our formal ally."

South Korea has agreed to pay substantially more money to the United States in order to defend itself from North Korea. Over the past many decades, the U.S. has been paid very little by South Korea, but last year, at the request of President Trump, South Korea paid $990,000,000.. — Donald J. Trump (@realDonaldTrump) August 7, 2019

On Wednesday, Trump tweeted that "South Korea has agreed to pay substantially more money to the United States in order to defend itself from North Korea. Over the past many decades, the U.S. has been paid very little by South Korea, but last year, at the request of President Trump, South Korea paid $990,000,000."

Trump went on to say that "talks have begun to further increase payments to the United States."

South Korea spends about 2.6% of its GDP on defense spending, more than most NATO allies, according to the Stockholm International Peace Research Institute. The US spends about 3.2% GDP on defense.

Seoul has also long reimbursed the US for various operating costs for the American troop presence there.

But Maxwell and others raised concerns that Trump could badly strain or even undermine the alliance.

"With Trump making these demands on South Korea, it could be a perfect storm to damage the alliance," Maxwell said.

'Inescapable distress'

Despite Trump's tweet saying talks on more payments had begun, a South Korean official said they haven't and added that a starting date hasn't even been set. The White House on Wednesday countered that at least some discussions are underway.

"As the President has indicated, discussions have begun to further increase South Korea's contributions to military defense," said a senior administration official. National security adviser John Bolton was in Seoul in late July.

While Trump directly tied South Korea's need to defend itself against North Korea to the increased payments he wants, he has otherwise dismissed Pyongyang's tests.

In the wake of July 30 missile launches that Kim said would cause "an inescapable distress" to targeted forces, Trump tweeted on August 2 that the missile tests "may be a United Nations violation," but didn't violate any agreement he had made.

Kim oversaw another launch early Tuesday morning local time and said it was a warning to the US and South Korea over their joint military drills, North Korean state-run KCNA reported Wednesday.

North Korea again fired projectiles — its fifth in just over two weeks -— into the sea early Saturday local time, according to US and South Korean officials.

A North Korean Foreign Ministry spokesman said the joint military drills were a "flagrant violation" of agreements, would "cause a backlash" and accused the US of increasing "hostile military tensions," KCNA said.

...Talks have begun to further increase payments to the United States. South Korea is a very wealthy nation that now feels an obligation to contribute to the military defense provided by the United States of America. The relationship between the two countries is a very good one! — Donald J. Trump (@realDonaldTrump) August 7, 2019

A senior defense department official traveling in Asia with Secretary of Defense Mark Esper said Wednesday that it was "not helpful to have provocative words like that."

The aide noted that Trump said he would end "the war games" and characterized those as "the larger scale offensively designed exercises, this is in no way a violation. We listen to their words, but ask them to stick to what they agreed."

Esper himself said Tuesday the launches wouldn't impact military exercises with South Korea.

Those exercises have been scaled down, however.

"We made some adjustments after the presidents' last meeting last year and we're still abiding by those.... But at the same time, we need to maintain our readiness and making sure that we're prepared," Esper said.

Klingner notes that since Trump first met with Kim in Singapore in June 2018, the allies have canceled 12 military exercises and put additional constraints on others, while Pyongyang put no limits on its own military exercises.

Esper also downplayed the missile tests, saying Tuesday that the US would not "overreact" to Pyongyang's latest launch of what are thought to be two short range ballistic missiles.

'Very impressive' missiles

In contrast, the UK on Tuesday said it is "deeply concerned" by North Korea's multiple ballistic missile launches. A foreign office spokesman said the launches are a "clear breach of UN Security Council Resolutions and pose a grave threat to our regional partners and global security."

Narang of MIT said North Korea's missiles "are very impressive," mentioning their trajectory, solid fuel and ability to maneuver in flight, which makes them hard to strike.

"This ends up being a nightmare for missile defenses," Narang said. "You can downplay it, but it obscures the fact that North Korea has been improving its missile capabilities. It's a real problem for regional missile defenses."