The South Korean marines were sent in after monsoon rains flooded a rural section of the country’s heartland last July. They were looking for missing residents in waist-high floodwaters, but they were not wearing life jackets. Nor did they have buoys or safety tubes.

When the ground gave way, five of them were swept away in the churning brown water and one, Lance Cpl. Chae Su-geun, disappeared downstream, yelling for help, and was later found dead.

Nearly a year later, the death of the 20-year-old marine has become an impeachment threat for South Korea’s leader, President Yoon Suk Yeol. And it has raised the prospect of political instability in the nation, a key United States ally in creating a bulwark against North Korea and China.

The South Korean military is no stranger to tragic accidents, but this latest episode has evolved into the first major political crisis for Mr. Yoon since his party’s crushing defeat in parliamentary elections last month. The career military officer who investigated Lance Corporal Chae’s death has accused the Defense Ministry of whitewashing the probe and absolving top military brass of responsibility — all under pressure from Mr. Yoon.

Mr. Yoon has not directly addressed the allegation, and last week the president vetoed a bill pushed through Parliament by the opposition calling for a special prosecutor to investigate the claim. The president wants government agencies like the police and prosecutors to finish investigating the various allegations before discussing other steps.

But there is wide public support for appointing a special prosecutor, surveys show, as many South Koreans have grown distrustful of Mr. Yoon and government prosecutors. Mr. Yoon’s opponents say that while prosecutors have launched criminal investigations into his critics and journalists accused of spreading “fake news,” they have not investigated allegations of corruption against his wife, Kim Keon Hee, with the same eagerness. (This and a string of other scandals contributed to Mr. Yoon’s poor showing in last month’s election.)

The opposition has threatened to begin impeachment proceedings against Mr. Yoon if he keeps resisting its demand.

“The Yoon regime should not forget lessons of history,” said Lee Jae-myung, the leader of the liberal opposition, referring to former presidents who have been imprisoned or impeached for corruption and abuse of power.

The opposition has a bigger majority in a newly elected Parliament that was inaugurated Thursday. It plans to pass another special-prosecutor bill but it remains to be seen whether it has the votes to override a presidential veto or enough public support and incriminating evidence against Mr. Yoon to begin impeachment proceedings against him.

Days after the death of Lance Corporal Chae, a probe launched by the South Korean Marine Corps concluded that he and his fellow marines had not been given life jackets or safety tubes. The knee-high rubber boots they were issued impeded their movement in the water. The military has admitted to the safety lapses.

The inquiry also concluded that eight supervisors, including Maj. Gen. Im Seong-geun, commander of the 1st Marine Division, were responsible for Lance Corporal Chae’s death through negligence. The then-defense minister, Lee Jong-sup, signed off on the findings to be forwarded, as required by law, to the national police for further investigation. He greenlighted the investigators’ plan to brief the news media.

“But in less than 24 hours, all the decisions were reversed, and everything turned into a mess,” said Col. Park Jung-hun, the top investigator.

Mr. Lee ordered Colonel Park to cancel the media briefing that had been planned for the next day. The Defense Ministry retracted the files Colonel Park had sent to the police. It later sent the police a revised version that named only two of the original eight, both lieutenant colonels, in connection with Lance Corporal Chae’s death.

Colonel Park has said that the top Marine commander told him that when Mr. Yoon learned of the colonel’s findings, he “flew into a rage” and called Mr. Lee to express his anger. (The commander denied making such a statement.) Colonel Park said the president’s reaction was followed by pressure from the Defense Ministry to expunge the names of top officers like Major General Im as criminal suspects from his report.

Mr. Yoon has not directly addressed the allegation, and his office has declined to comment, pending investigations by the police and the Corruption Investigation Office For High-Ranking Officials, a government agency. Mr. Lee has denied being pressured by Mr. Yoon’s office. And analysts have struggled to explain why Mr. Yoon may have taken such an action.

But Colonel Park has stood by his allegation. The Defense Ministry has moved to court-martial him on charges of insubordination. Officials say that he ignored an order to delay handing over the investigation files to the police. The colonel says that the files were already en route to the police when he received the order. He has said he is being persecuted for resisting pressure to remove the names of senior officers from his report.

During Colonel Park’s court-martial trial this month, Yoo Jae-eun, an aide to the defense minister, was called to testify. She said that when she called the colonel under Mr. Lee’s instruction, she suggested that he not name any criminal suspects or cite any suspected crime in his report. She insisted that the suggestion was meant not as undue pressure but as “one of the options” for the colonel to consider.

Another marine who was swept into floodwaters and has since been discharged has sued Major General Im for professional negligence. He claims that his unit was ordered into the dangerous waters to please the general, whose obsession with publicity he said guided his units’ disaster-relief activities. Major General Im has called the lawsuit “libelous.”

Mr. Yoon has expressed condolences over Lance Corporal Chae’s death and criticized the marines’ operation in the floodwaters, but he has been silent on the allegation of illegal pressure. But South Koreans have often found decisions by Mr. Yoon “mysterious,” Lee Jin-young, an editorial writer at the conservative daily Dong-A Ilbo, said in her column. When Mr. Yoon made “impulsive” decisions, his staff lacked the courage to withstand his “rage” and speak up, she said.

“Instead, when the president hits the wrong target, they draw a bull’s-eye around it,” Ms. Lee wrote. “As this repeats, scandals erupt and his approval ratings fall.”