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.