The peasant union official who early this week reported the gruesome death squad killing of his 14-year-old son and two other Salvadoran youths today admitted that the story was false.

The admission by Alirio Montes, the publicity director of the U.S.-supported Salvadoran Communal Union, was made much to the embarrassment of the U.S. Embassy here and appeared likely to exacerbate tensions over the incident between the embassy and the government of President Jose Napoleon Duarte.

On Tuesday, the embassy had sharply condemned the alleged killing in a communique that apparently was based only on information supplied by Montes and was not coordinated with the government. The communique called on Duarte to take swift action in the case.

In a news conference yesterday, Duarte publicly reprimanded the embassy for issuing a statement dealing with the "national affairs" of El Salvador, particularly since the details of the incident had not yet been verified by his government. Duarte said he had called in U.S. Ambassador Thomas Pickering to protest the action.

Today, as a distressed Montes confessed to union officials and foreign reporters that he had "only imagined" his son's death, embarrassed U.S. Embassy officials sought to defend their original communique by stating that, although the facts on which it was based were erroneous, the expressed outrage at the alleged killing was genuine and made in "good faith."

"We are not repentant," said a U.S. official who asked that his name not be used, "save to the extent the communique failed to represent certain facts."

"Obviously, that this event didn't happen makes the communique inaccurate," the official said, "But the communique is not a false reflection of our position on the activities of death squads."

The official said that the embassy had no intention of issuing another communique on the matter and that it was not ruling out issuing other statements about violence in the country despite Duarte's public rebuke yesterday. "We will make such a determination on the basis of the situation at the time it occurs," the official said.

The Montes incident coincides with an ongoing effort by the Reagan administration to counter criticism in the United States that its Central American policies lack an adequate human rights component. Policy opponents in Congress have charged that the administration's emphasis on military assistance to defeat leftist guerrillas here has diluted attempts to improve the Salvadoran Army's human rights record and to send a message of unequivocal censure to rightist death squads.

The death squads, believed to be tied to rightist political and business forces here and to some elements in the armed forces, had lessened their activities following Duarte's election in May. Duarte's unprecedented peace meeting with leftist leaders Oct. 15, however, had prompted a public threat against his life by the Secret Anticommunist Army. Montes' allegation appeared to have been the first reported killing claimed by the clandestine rightist group since that threat.

The original embassy communique, which was personally approved by Ambassador Pickering, according to embassy officials, expressed U.S. outrage "that once again murderous thugs masquerading as paramilitary 'patriots' have taken innocent life." It called the alleged killing of Montes' 14-year-old son Boris a "depraved tactic" of attacking a father through his children that brought to mind the "vile practices of Stalin and Hitler."

In his press conference yesterday Duarte indicated that it was his investigation into the story begun after the issuance of the embassy statement that unearthed indications that it never happened -- at least not the way Montes had told it first to a U.S. Embassy labor attache, Edward Baez, and later to reporters.

When interviewed two days ago at his union headquarters in the town of Santa Tecla just outside the capital, Montes said that he received a call just before dawn Saturday telling him that his son had been killed and his body dumped near Mariona Prison.

Montes claimed that when he drove to the area around the prison, a traditional dumping ground for death squad victims, he found the body of his son and two other youths. He said all three had been shot at close range and had the initials ESA, the Spanish initials of the Secret Anticommunist Army, carved in their foreheads.

Confronted today in a second interview after he had been interrogated by union officials who previously had corroborated his story, Montes first told reporters that he had in fact seen the three bodies, but that it turned out that the one he originally thought was his son was not. Under repeated questioning about discrepancies in his story, Montes said finally that it had not happened and that he had "only imagined it" because of the "pressure" he had been under in recent months due to previous death threats. He also said he might have been suffering from taking too many tranquilizers that night.

With a gun stuck in his waistband, the burly 41-year-old union official seemed distressed and obviously confused today. He repeatedly changed his story while insisting that all he knew was that his son had in fact "disappeared." But, he said, he now knew for a fact that his son was alive because he had talked to him by telephone this morning.