SEOUL, South Korea — A week ago, things could not have been going better for President Moon Jae-in of South Korea. He was successfully arranging a meeting between North Korea’s leader, Kim Jong-un, and President Trump. His approval ratings at home were soaring. The tone had changed so much that Mr. Trump had even called Mr. Kim “very honorable.”

Now, the matchmaking role that has defined Mr. Moon’s presidency is in doubt.

After months of unusual bonhomie, North Korea withdrew on Wednesday from talks with South Korea and threatened to cancel the planned June 12 summit meeting between Mr. Kim and Mr. Trump, which Mr. Moon’s aides have spent months trying to set up.

For Mr. Moon, the North’s reversal brought home the difficulties in playing matchmaker between his country’s most fearsome foe and its most important ally, two countries run by impulsive and often unpredictable leaders.

It shows the extraordinarily difficult challenge that Mr. Moon confronts. He faces skepticism from both Pyongyang and Washington that he can be an honest broker. North Korea still considers South Korea an American stooge. In the United States, conservatives who have the president’s ear worry that progressive South Korean leaders like Mr. Moon will ease sanctions, breaking ranks with Washington in their eagerness to reconcile with the North.

“A matchmaker can succeed when boy and girl like each other,” said Moon Seong-mook, a senior analyst at the Korea Research Institute for National Strategy in Seoul. “But the United States and North Korea have very different ideas on how to achieve denuclearization.”

It remains unclear whether the North’s sudden shift in attitude signaled a return to brinkmanship or mere posturing before the summit meeting, which is slated to take place in Singapore.

On Thursday, Pyongyang dug in its heels, calling Mr. Moon’s government “impudent” and “shameless” for asking for inter-Korean talks while it continued joint military exercises with the United States. The two allies started their “Max Thunder” air force drill last week, which the North condemned as a rehearsal for invasion.

“It won’t be easy to sit down again with the current government of the South until it resolves the grave situation,” Ri Son-gwon, a senior North Korean negotiator, told the North’s official Korean Central News Agency.

While most South Koreans support Mr. Moon’s role as an intermediary, North Korea’s actions on Wednesday give political ammunition to his conservative enemies, who call him a naïve amateur who has fallen for Pyongyang’s trap of “false peace.” They fear that Mr. Moon will not denuclearize the North, and will weaken Seoul’s alliance with Washington.

North Korea’s reversal has already dampened some of the optimism that pervaded South Korea after Mr. Moon’s dramatic meeting with Mr. Kim on the inter-Korean border on April 27. His party had been hoping to benefit politically from the Singapore meeting, which would take place a day before elections of mayors and provincial governors in South Korea. Mr. Moon’s North Korea diplomacy has loomed large over the contests.

Mr. Moon’s government vowed on Thursday to “step up a mediator’s role,” urging North Korea and the United States to “respect each other” and “think in the other’s shoes,” despite occasional setbacks.

“The situation we have is part of the long and hard process of creating the same painting,” said Mr. Moon’s spokesman, Yoon Young-chan.

North Korea and the United States have the same name for that painting: a “nuclear-free Korean Peninsula.” But they differ sharply on the best way to complete it.

The Trump administration, particularly the national security adviser, John R. Bolton, wants North Korea to dismantle its nuclear program as soon as possible. Only when denuclearization has become irreversible, it says, will the United States ease sanctions and reward the North economically.

But North Korea says it will not bargain away its nuclear weapons for the sake of its economic future. Mr. Kim insists that he will take only “phased” steps toward denuclearization, and that Washington must match each with “synchronized” measures to satisfy North Korean demands for security guarantees. These include normalized ties and a peace treaty with the United States, as well as the lifting of sanctions.

“There is a huge gap between the North and the United States over denuclearization,” said Lee Seong-hyon, a research fellow at the Sejong Institute in South Korea. “There should be a lot of soul-searching going on in Seoul over whether it has been a mediator and communicator trusted by both sides.”

Mr. Moon has repeatedly argued that Mr. Kim would be willing to trade away his nuclear weapons for the right incentives. He called Mr. Kim “open-minded,” “frank” and “courteous.”

“Through many hours of frank and serious discussions with Chairman Kim, I could again and again confirm his willingness for complete denuclearization,” Mr. Moon said last week.

His government hopes that North Korea and the United States can meet halfway by exchanging denuclearization with security guarantees in a “phased” manner, as the North demands, while carrying out the deal quickly, as Washington wants — perhaps before the end of Mr. Trump’s term in early 2021.

South Korean officials are confident that such a deal is possible. They say that Mr. Kim is desperate to rebuild his nation’s economy and knows that he cannot do so without resolving the nuclear crisis, and that Mr. Trump is eager to make a deal before the midterm elections in November.

But as Mr. Moon acknowledged, “the devil will be in the details” — particularly who should make the first move and how to verify that promises are kept.

When China’s premier, Li Keqiang, met the South Korean leader in Tokyo last week, he warned that North Korea thought it was doing its part to show its intention to denuclearize — by unilaterally announcing a moratorium on nuclear and missile tests and by inviting outsiders to monitor the shutdown of its nuclear test site.

Pyongyang was “waiting for a corresponding feedback from the United States,” Mr. Li was quoted by South Korean officials as saying. Instead, North Korea saw the United States and South Korea pressing ahead with their annual military exercises.

Mr. Bolton also called for the removal not only of nuclear arms but also of chemical and biological weapons from North Korea.

This week, North Korea pushed back, threatening to cancel the summit meeting with Mr. Trump.

The developments showed how delicate Mr. Moon’s task is in bringing Mr. Trump and Mr. Kim together — and getting them to see eye to eye.

If Mr. Kim does not cooperate, Mr. Bolton has warned, it could be a “pretty short meeting” in Singapore.

“Then we will see the crisis rapidly rising on the Korean Peninsula,” said Lee Byong-chul, a senior fellow at the Institute for Peace and Cooperation in Seoul. “The mediating role by South Korea and China has become more urgent than ever.”