SEOUL, South Korea — President Moon Jae-in of South Korea told President Trump on Thursday that he planned to send a special envoy to North Korea as part of his effort to broker talks between the United States and the North on ending its nuclear weapons program.

President Moon’s office said he talked with Mr. Trump on the phone on Thursday to discuss joint strategies, based upon the discussions Mr. Moon and his aides have held with senior North Korean officials who visited the South last month to attend the opening and closing ceremonies of the Olympics in Pyeongchang.

“The two heads of state agreed to keep the momentum in South-North Korean dialogue and continue efforts to use it to lead to the denuclearization of the Korean Peninsula,” Mr. Moon’s office said in a statement. “To that end, President Moon notified President Trump that his government will soon send a special envoy to the North to confirm the discussions it has held with the high-level North Korean delegates.”

By sending a special envoy to North Korea, Mr. Moon was also reciprocating the visit to the South by Kim Yo-jong, the sister and trusted aide of the North Korean leader, Kim Jong-un, it said. Mr. Kim sent his sister to attend the opening ceremony of the Olympics last month and to deliver his invitation to Mr. Moon to visit the North for an inter-Korean summit meeting.

Mr. Kim sent another high-level delegation, led by his former spy chief, Kim Yong-chol, to attend the closing ceremony on Sunday. The delegates told Mr. Moon that North Korea was willing to start talks with Washington, although it remained unclear whether it was ready to discuss denuclearization, as Washington has demanded.

Mr. Moon is eager to use the diplomatic opening created by the Olympics and the visits of the North Korean envoys to help arrange for the United States and North Korea to sit down for talks, as well as to improve inter-Korean relations.

His immediate challenge is how to narrow the wide gap between the United States and North Korea over the terms under which they would start a dialogue.

North Korea says it will not bargain away its nuclear weapons, and it insists that the United States first recognize it as a nuclear power. Only then, the North Koreans say, will they sit down with American officials to discuss mutual arms reduction on the Korean Peninsula.

On Monday, Mr. Trump said the Americans “want to talk also” — but “only under the right conditions.” “Otherwise,” he said, “we’re not talking.”

That has been the consistent American stance since the administration of President Barack Obama, although Mr. Trump, unlike Mr. Obama, has openly threatened to use military force to end the nuclear crisis. For its part, North Korea drastically escalated the stakes by conducting its sixth and most powerful nuclear test and test-firing intercontinental ballistic missiles last year.

Washington insists that it is not interested in talks unless they deal with denuclearizing the North. United States officials say the North has failed to abide by agreements in past negotiations, and they demand that the North first show its sincerity before talks can start.

Mr. Moon has said that if North Korea announced a freeze in its nuclear and missile tests, it would help start talks between the North and the United States.

But even if North Korea agrees to such a freeze, it is widely expected to demand that the United States reciprocate, perhaps by suspending its annual joint military exercises with South Korea, analysts said. It remains unclear whether Mr. Trump is ready to offer such a concession. Mr. Moon’s government says that the allies will announce their plans regarding the joint war games after the Paralympics end in Pyeongchang on March 18.

Mr. Moon has urged the United States and North Korea to soften their uncompromising stances so that talks could start on defusing the crisis, which appeared to push the Korean Peninsula to the brink of war in the past year.

“The United States needs to lower the threshold for dialogue, and North Korea should express a willingness to denuclearize,” Mr. Moon said on Monday.

Mr. Moon, a longtime proponent of reconciliation with North Korea, wants to accept Kim Jong-un’s proposal for an early summit meeting to improve ties and further lower tensions, analysts have said. But to make his inter-Korean agenda sustainable, Mr. Moon needs the United States and North Korea to make progress in denuclearization talks.