U.S. officials here are investigating the possibility that a young American picked up for questioning by Salvadoran soldiers last month and reportedly killed while trying to escape may have been murdered.

The officials said in interviews this morning that they were concerned about apparent discrepancies between the soldiers' initial account of the Oct. 13 killing of Michael David Kline, 21, and later medical reports that raise the possibility he was summarily shot.

The death of Kline, described as a "drifter," comes as the Reagan administration is already under heavy pressure from Congress to show that the government it backs here is making progress in investigating and prosecuting the murders of four American churchwomen in December 1980 and two U.S. labor advisers a month later.

Members of the Salvadoran military have been implicated in both cases, and the United States has had only limited success in pushing for substantive investigations and prosecutions. This week, a Salvadoran judge ruled that evidence against five National Guard soldiers held in connection with the deaths of the four women was sufficient for trial.

Kline's death has placed the U.S. Embassy here again in the difficult position of pressing for evidence that could damage overall U.S. policy goals in El Salvador by making even more difficult the certification of human rights improvement demanded by Congress.

In a speech last month and later interviews U.S. Ambassador Deane Hinton warned that Washington's economic and military aid, needed by this country's rulers in their fight against leftist insurgents, could be cut off over the human rights issue in general and the American murder cases in particular.

A U.S. diplomat authorized to speak about the case described Kline's death as "sensitive" and said, "The important thing now is how it is resolved by the Salvadoran authorities." A new examination of Kline's body by Salvadoran doctors at the military hospital is under way.

"We are trying to verify the soldiers' story," the diplomat said. "It could be he did try to escape and maybe they dropped him and then came up close to finish him off."

Much about Kline is a mystery, including most details about his background, his motives for traveling to one of the most wartorn provinces in El Salvador, and why he was carrying $500 in traveler's checks but no passport or other documents.

But there is also much about Kline's death that has the ring of the commonplace in this war where it is estimated that more than 35,000 people have died in three years.

The killings of Americans, as one Western diplomat put it, tend to "synthesize the whole problem here" by drawing attention to the conditions in which many Salvadorans die.

The picture of Kline put together by U.S. officials is of a young "drifter" born in Tijuana, Mexico, to a German-born mother who has returned to her home near Hamburg and a father who lives in Chicago but who, according to the U.S. account, was said to be uninterested in the case.

A U.S. consular report from West Germany said Kline's mother, Renate Margaret Kline, believed he wanted to be a journalist.

There are spotty records of Kline buying traveler's checks in Alaska earlier this year, leaving Costa Rica in May, and reporting the loss of the checks and a passport in Cancun, Mexico, on Sept. 6. He apparently found them again before traveling to Guatemala later in the month, then crossed into El Salvador on Oct. 11, according to Guatemalan records given U.S. officials. The documents were reportedly gone when he died.

Kline was not positively identified as a U.S. citizen until Monday, when dental records arrived here. It was not until then, U.S. officials said, that they were able to press the investigation.

First word of Kline's death came when the head of El Salvador's Armed Forces Press Committee, Col. Marco Aurelio Gonzales, took the unusual step of calling a press conference here Oct. 15 to tell foreign journalists that a "gringo mercenary," possibly an American or Canadian, had been killed by government troops in Morazan province.

The press officer reportedly claimed at one point during the conference that Kline had seized one of the soldiers' guns and fired at them before they killed him, but this is nowhere corroborated by the basic account of what happened. This account comes from Army Sgt. Jose Desposorio Lopez, who was directly involved in the incident.

As U.S. officials recount the story from Lopez's affidavit and an interview with him on Oct. 21, Kline was riding a bus that runs from the city of San Miguel to the garrison town of San Francisco Gotera about 100 miles northeast of the capital when it was stopped by the army at a routine checkpoint.

Lopez found Kline suspicious on the basis of his "long hair, dirty clothes and rubber sandals" and lack of identification papers, he said in his report. Kline was ordered detained.

Kline was taken to the bivouac at the checkpoint and his belongings searched. Initial accounts based on the press conference cited the report that he carried a knapsack, an air mattress, insect repellent, medicine (Alka-Seltzer) and lubricating oil that "could be used for cleaning a weapon" as evidence that he might be a guerrilla.

U.S. officials say that Lopez told them Kline spoke little or no Spanish and did not seem to understand everything he was told. He carried no identification except for the traveler's checks, Lopez reported.

Lopez said he, a soldier named Hector Rubina Reyes and another referred to only as "Cristobal" flagged down a pickup truck to take them to headquarters at San Francisco Gotera.

According to Lopez' account the truck slowed about four miles down the road and Kline lunged for one of the soldiers' rifles. When he failed to get it he jumped off and began running uphill.

Lopez told U.S. officials Kline was ordered to stop, but kept running and was shot down at a distance of about 30 feet.

"We have problems with the sergeant's story," said one embassy official. "He reports three shots -- two in the neck and one in the back, all from the back."

But photographs of the body and the first medical report on the case, written the day after the killing, showed that one of the shots was in the head, from front to back, according to U.S. officials.

Moreover, the doctor who wrote that report noted that there were no powder burns on the wound in Kline's back, but he did not mention the state of the wound in his head (which has yet to be determined conclusively) and did not mention the third wound in the body at all.

The officials said they are awaiting the new report from the military hospital before deciding what further steps to take in the investigation.