The South Korean and United States militaries view their annual drills in South Korea as more critical than ever. The stakes have risen dramatically as North Korea has gained battlefield expertise with drones and modern warfare by deploying troops to support Russia’s war in Ukraine.

The summer exercise had barely begun on Monday when President Trump denounced it, dealing yet another blow to the seven-decade-old alliance between Washington and Seoul. Under Mr. Trump, bilateral relations have already come under immense strain from ​his punishing tariffs on South Korean exports.​ And his transactional diplomacy has frustrated South Korea, most recently when he appeared to put Saudi Arabia on the path to enriching nuclear fuel on its own soil, a demand Seoul has made for years.

In recent years, North Korea has ​not only expanded its nuclear arsenal but also repeatedly threatened ​to use it against South ​Korea, labeling its neighbor ​a “most ​hostile enemy.” Its leader, Kim Jong-un, has also forged a mutual defense treaty with Moscow, dispatching troops and​ weapons to ​support Russia’s war against Ukraine. Despite these escalations, Mr. Trump, in a social media post, characterized North Korea as “unthreatening and respectful” while boasting of his “very good relationship” with Mr. Kim.​

In the same post, he ​also criticized the decades-old joint military drills with South Korea as “not only costly” but “totally inappropriate and hostile” toward North Korea.

“I am not happy with the fact that the United States has, long ago, agreed to participate in Joint Military Exercises with South Korea,” he said. “Based on the fact that it is too late to cancel, I have instructed Secretary of War, Pete Hegseth, to substantially reduce the Joint Military Exercises!”

If implemented, the directive would mark Mr. Trump’s first-known concrete overture toward North Korea in his second term. However, it remains unclear whether Mr. Kim will embrace the gesture.

Throughout his political career, Mr. Trump has treated the alliance as a​ bad bargain for Americans, frequently accusing Seoul of failing to pay its fair share for the U.S. troops stationed in South Korea — who act as a deterrent to North Korea. During his first term, he unilaterally canceled or downscaled major drills, calling them “tremendously expensive” and “​very provocative.”​ That concession helped facilitate three summit meetings with Mr. Kim but failed to roll back his nuclear ambitions.

Since returning to the White House, Mr. Trump has signaled a desire to renew that personal diplomacy. Over the weekend, he posted a 2019 photograph of himself and Mr. Kim at the inter-Korean border, writing, “Kim Jong Un and I get along GREAT!”

“Trump’s description of the D.P.R.K. as ‘unthreatening and respectful’ is alarming to allies, who have watched the regime steadily improve its missile and nuclear capabilities, while also gaining an additional patron in Russia for its support in the war on Ukraine,” said Emma Chanlett-Avery, the deputy director at the Asia Society Policy Institute, referring to North Korea’s full name, the Democratic People’s Republic of Korea.​

Th​is summer’s 11-day Ulchi Freedom Shield exercise was designed to adapt to these shifting dynamics​, incorporating lessons learned from recent conflicts, including from Ukraine. Lt. Gen. Joseph E. Hilbert of the U.S. Eighth Army noted that the maneuvers would ​also test “the alliance’s ability to rapidly project combat power and secure key terrain within the First Island Chain”​ —​ a long Pacific archipelago seen by the U.S. military as a strategic frontier against China’s expansive territorial claims.

South Korea’s government declined to comment on Mr. Trump’s post, which also included scolding Seoul for not helping “denuclearize” Iran. While the government confirmed that the drills had begun as scheduled, the country’s defense establishment was deeply rattled. Mr. Trump’s directive fueled growing fears​ that the alliance is hollowing out.

“South Korean conservatives​, in particular, will see the alliance turning into a zombie, ​considerably losing its old strategic objectives and political energy under Trump,” said Lee Byong-chul, an analyst at the Institute for Far Eastern Studies in Seoul.

Mr. Trump’s overture toward North Korea, however, is not entirely unwelcome for his South Korean counterpart, Lee Jae​ Myung, analysts said. A staunch proponent of inter-Korean reconciliation, Mr. Lee has urged Mr. Trump to ease tensions on the Korean Peninsula through direct talks with Mr. Kim. ​North Korea has long cited the joint drills as a major stumbling block to such efforts, calling them “a rehearsal for an aggressive war.”

“Now that Trump has made scaling back these exercises official U.S. policy, the Lee administration is likely secretly rejoicing,” said Mr. Lee, the analyst. “It’s intriguing that Lee and Trump — despite having completely different underlying motives — could see their approaches toward North Korea converge.”

But a second round of Trump-Kim diplomacy faces much steeper hurdles than it did in 2018. North Korea is now a de facto nuclear state that has been bolstered by economic lifelines and diplomatic leverage from Moscow and Beijing. While Mr. Kim has noted that he retains “a good memory” of Mr. Trump, he has emphasized that North Korea would resume talks ​only if Washington abandons its insistence on denuclearization.