SEOUL — ​President Moon Jae-in of South Korea has a message for the United States: President Biden needs to engage now with North Korea.

In an interview with The New York Times, Mr. Moon pushed the American leader to kick-start negotiations with the government of Kim Jong-un, the leader of North Korea, after two years in which diplomatic progress stalled, even reversed. Denuclearization, the South Korean president said, was a “matter of survival” for his country.

He also urged the United States to cooperate with China on North Korea and other issues of global concern, including climate change. The deteriorating relations between the superpowers, he said, could undermine any negotiations over denuclearization.

“If tensions between the United States and China intensify, North Korea can take advantage of it and capitalize on it,” Mr. Moon said.

It was part plea, part sales pitch from Mr. Moon, who sat down with The Times as the United States tries to rebuild its relationships in the region with an eye to countering China’s influence, and North Korea builds up its nuclear arsenal. Mr. Moon, who is set to meet with Mr. Biden next month in Washington, appeared ready to step once again into the role of mediator between the two sides.

In the interview, Mr. Moon ​was proud of his deft diplomatic maneuvering in 2018, when he steered the two unpredictable leaders of North Korea and the United States to meet in person. He was also pragmatic, tacitly acknowledging that ​his work to achieve denuclearization and ​peace on the Korean Peninsula has since unraveled.

President Donald J. Trump left office without removing a single North Korean nuclear warhead. Mr. Kim has resumed weapons tests. ​

“He beat around the bush and failed to pull it through,” Mr. Moon said of Mr. Trump’s efforts on North Korea. “The most important starting point for both governments is to have the will for dialogue and to sit down face to face at an early date.”

Now in his final year in office, Mr. Moon is determined to start all over again​ — and knows he faces a very different leader in Mr. Biden.

Mr. Moon bet on Mr. Trump’s style, emphasizing personality-driven “top-down diplomacy” through one-on-one meetings with Mr. Kim. Mr. Biden, he said, was returning to the traditional “bottom-up” approach in which negotiators haggle over details before seeking approval from their bosses.

“I hope that Biden will go down as a historic president that has achieved substantive and irreversible progress for the complete denuclearization and peace settlement on the Korean Peninsula,” Mr. Moon said in the interview from Sangchunjae, a traditional hanok on the grounds of the executive residence, Blue House.

Mr. Moon’s visit to Washington comes at a crucial moment. The Biden administration is wrapping up its monthslong policy review of North Korea, one of the most pressing geopolitical issues for the United States.

​Mr. Biden ​has started reversing many of his predecessor’s foreign policy decisions​. But Mr. Moon ​warned that it would be a mistake to kill the 2018 Singapore agreement between Mr. Trump and Mr. Kim ​that set out broad goals for denuclearizing the Korean Peninsula. ​

“I believe that if we build on what President Trump has left, we will see this effort come to fruition under Biden’s leadership,” he said.

Mr. Moon called for the United States and North Korea to ​move in “gradual and phased” ​steps toward denuclearization​, exchanging concessions and incentives “simultaneously”​ along the way. It was a well-worn script for Mr. Moon, who paused occasionally during the interview to reference his notes and punctuated his speech with small yet resolute hand gestures.

Some past American negotiators and Mr. Moon’s conservative critics dismiss such a strategy, saying North Korea would stall and undermine international sanctions, the best leverage Washington has against the impoverished country. In its annual threat assessment released last week, the United States’ director of national intelligence said Mr. Kim “believes that over time he will gain international acceptance and respect as a nuclear power.”

But Mr. Moon’s team argues that the phased approach is the most realistic, even if it is imperfect. As his administration sees it, North Korea would never give up its arsenal in one quick deal, lest the regime lose its only bargaining chip with Washington.

The key​​, Mr. Moon said, is for the United States and North Korea to work out a “mutually trusted road map.”

American negotiators under Mr. Trump never made it to that point. Both sides could not even agree on a first step for the North and what reward Washington would provide in return.

Mr. Moon is not only scrambling to salvage his “Korean Peninsula Peace Process” but also arguably his greatest diplomatic legacy.

As his North Korea policy has faltered, critics have called him a naïve pacifist who bet too much on Mr. Kim’s unproven commitment to denuclearization.

“His good intentions brought bad consequences,” said Kim Sung-han, a professor at Korea University. “His mediation has not worked nor do we have progress in denuclearization. His time is running out.”

Since the negotiations have stalled, Mr. Moon’s troubles at home have mounted. His approval ratings have plunged to record lows amid real-estate and other scandals. This month, angry voters delivered crushing defeats to his Democratic Party in the mayoral elections in South Korea’s two largest cities.

That is a sharp turn of fortune from the start of his administration, when Mr. Moon parlayed a hair-raising geopolitical crisis into a signature policy initiative.

“When I took office back in 2017, we were really concerned about the possibility of war breaking out once again on the Korean Peninsula,” he said.

Four days into his tenure, North Korea launched its Hwasong-12 intermediate-range ballistic missile that it said could target Hawaii and Alaska. Then the North tested a hydrogen bomb and three intercontinental ballistic missiles. In response, Mr. Trump threatened “fire and fury,” as American Navy carrier groups steamed toward the peninsula.

Mr. Moon’s first diplomatic win came when Mr. Kim accepted his invitation to send a delegation to the 2018 Winter Olympics in Pyeongchang, South Korea. Soon after, Mr. Moon met with Mr. Kim on the heavily armed inter-Korean border.

During that meeting, Mr. Moon said the North Korean dictator intimated that disarmament was a real possibility. “If safety can be guaranteed without nuclear weapons, why would I struggle to hold onto them even at the cost of sanctions?” Mr. Moon recalled Mr. Kim saying.

He said he made that pitch to Mr. Trump, imploring him to meet Mr. Kim. At their made-for-TV summit in Singapore, Mr. Trump promised “security guarantees” for North Korea while Mr. Kim committed to “work toward complete denuclearization of the Korean Peninsula.”

“It’s clearly an achievement for President Trump that he held the first-ever summit meeting between North Korea and the United States,” he said.

But Mr. Moon also lamented that Mr. Trump never followed through, after declaring that “there is no longer a Nuclear Threat from North Korea.” When Mr. Kim and Mr. Trump met again in 2019 in Hanoi, Vietnam, the negotiations went nowhere, and the men left without an agreement on how to move forward with the Singapore deal.

While Mr. Moon was careful to dole out praise for Mr. Trump, he also seemed frustrated by the former president’s erratic behavior and Twitter diplomacy. Mr. Trump canceled or downsized the annual joint military drills that the United States conducts with the South and demanded what Mr. Moon called an “excessive amount” to keep 28,500 American troops in South Korea.

Mr. Moon said he had decided to suspend negotiations over the so-called defense cost-sharing agreement during Mr. Trump’s last months in office. South Korea was willing to pay more, given its growing economic size, but Mr. Trump’s demands violated the foundation of the two countries’ relationship.

“His demand lacked reasonable and rational calculation,” Mr. Moon said.

The fact, he said, that Washington and Seoul could strike a deal within 46 days of Mr. Biden’s inauguration was a “clear testament to the importance President Biden attaches to” the alliance.

Mr. Moon is hopeful about the progress the new American leader can make on North Korea, although any significant breakthrough may be unrealistic, given the deep mistrust between Washington and Pyongyang.

Mr. Biden said last month that he was “prepared for some form of diplomacy” with North Korea, but that “it has to be conditioned upon the end result of denuclearization.”

North Korea has offered ideas on a phased approach starting with the demolition of its only-known nuclear test site, followed by the dismantling of a rocket engine test facility and the nuclear complex in Yongbyon north of Pyongyang.

Mr. Moon said he believed such steps, if matched with American concessions, could lead to the removal of the North’s more prized assets, like I.C.B.M.s. In that scenario, he said, the move toward complete denuclearization becomes “irreversible.”

“This dialogue and diplomacy can lead to denuclearization,” he said. “If both sides learn from the failure in Hanoi and put their heads together for more realistic ideas, I am confident that they can find a solution.”