SEOUL — Washington is walking a fine line between South Korea’s conservative leaders and leftist forces anxious to see President Yoon ousted by a high court accepting the impeachment motion voted by the national assembly.

At the center of American diplomacy here, the acting ambassador, Joseph Yun, has been interacting with the opposition Democratic Party, or Minju, that rammed Mr. Yoon’s impeachment through the assembly after he issued a martial law decree in December that the legislators quickly voted down. With the constitutional court gearing to accept or reject the motion, the ambassador has given the impression of siding with the Minju in its quest for a peace agreement in place of the armistice that ended the Korean War in 1953.

A veteran diplomat who served in the American embassy here during the George W. Bush administration and then was in charge of North Korea issues during the first Trump presidency, Mr. Yun was named acting ambassador by President Biden shortly before President Trump’s inauguration in January.

In the spirit of rounding up support for talks with the North, the assembly invited Mr. Yun to the opening of a Korea-U.S. Congressional Alliance dedicated to fostering ties with the American Congress. To the delight of Minju leaders, he was optimistic about yet another summit between Mr. Trump and North Korea’s leader, Kim Jong-un, whom Mr. Trump saw three times during his first term and has made clear he would like to meet again.

As South Korea’s biggest-selling newspaper, Chosun Ilbo, reported, Mr Yun said Messrs. Trump and Kim “established a framework for negotiations” at their first summit in Singapore in June 2018 and then again at Hanoi in February 2019.

Mr. Yun did not have to say that the Hanoi summit ended abruptly when Mr. Trump cut off the conversation after Mr. Kim balked at giving up his nuclear program. He added, though, that “the likely approach would be to build on those past meetings as a foundation for renewed talks.”

Despite the failure of the Hanoi summit, according to Chosun Ilbo, Mr. Yun’s comments “suggested that President Trump might again consider holding a U.S.-North Korea summit in Singapore or Vietnam.” And, to allay Korean concerns that Mr. Trump might leave Seoul out of the dialogue, he said Washington “recognized the need for Seoul’s involvement in renewed talks” and “future negotiations with North Korea would not sideline Seoul.”

The focus on the search for a fourth Trump-Kim meeting, though, upsets Korean conservatives, who see the Minju as eager to exploit the Korea-U.S. Congressional Alliance as a channel for forming ties with members of the American Congress who have long been pressing for legislation calling for diplomatic relations between Washington and Pyongyang and a peace treaty in place of the armistice that ended the Korean War in 1953.

The national assembly speaker, Woo Won-sik, a long-time leftist activist, led the assembly in impeaching Mr. Yoon and then led a delegation to Beijing to see President Xi and tell the Chinese all about what they had accomplished.

Then, in a show of balancing relations, receiving Mr. Yun at his office, Mr. Woo promised to lead another delegation to Washington to explain “the stable situation” in South Korea. The inference was that he hoped to persuade Americans to go along with a deal with the North for withdrawing some of America’s 28,500 troops from South Korea.

In fact, many Minju members are long-time leftists. One of them, Park Sun-won, over lunch with Mr. Yun, let him know that he had nominated Mr. Trump for the Nobel Peace Prize in an obvious ploy for the president’s favor. Floor leader of the Minju in the assembly, Mr. Park is also remembered for his days as an anti-American activist, when he joined a group that “occupied” the U.S. Cultural Center at Seoul, leading to its closure.

Another Minju assembly member, Jung Chung-rae, was sentenced to prison in 1989 for setting an explosive device at the residence of the American ambassador. No one was injured, but he’s been denied American visas since then.