The engineer who fought to stop the fatal launch of the shuttle Challenger, but who was overruled by his company and NASA officials, yesterday became the center of a tug-of-war over who would hear his potentially dramatic and damning testimony about the tragedy.

Allan J. McDonald, in charge of the solid-booster rocket program at Morton Thiokol Inc., makers of the shuttle's boosters, came to town yesterday apparently prepared to speak to a private meeting of senators on Capitol Hill.

But the day ended with scores of reporters and photographers in an empty hallway, with six senators sitting in one room while the engineer sat in another telling the senators over a telephone speaker that he did not want to meet with them, despite flying 2,000 miles to do so. He said he would rather accept a fresh invitation to tell his story to the president's commission investigating the explosion.

Several senators who spoke with McDonald Wednesday said he was eager to tell his tale -- of his refusal to approve the launch, of the evidence from at least one prior mission that launching in chilly temperatures could be disastrous, and of the reversal of NASA's procedures on launches, from a reticent, show-me-why-it's-safe attitude to one of all-out pressure to get the craft in the air.

But he was fast becoming a highly sought-after figure in the investigation. So McDonald quickly found himself in deep water over who to tell what to.

What triggered his rising fame was what he said, and what was leaked from his testimony, in a closed session of the presidential commission, which is headed by former secretary of state William P. Rogers. He told of his vehement argument against the launch and of Thiokol engineers' determination that the mission was too dangerous to try.

That was Friday morning. By the following Wednesday evening four senators were on the phone with him, even as his story was leaking out to the news media. According to Sens. Ernest F. Hollings (D-S.C.) and Donald W. Riegle Jr. (D-Mich.), who spoke with McDonald, the engineer was upset.

"Mr. McDonald. . . told me that he was totally distressed with the hearings he had, in the sense that it was an off-the-record hearing. . . before the Rogers commission," Hollings said. McDonald said pieces of his story were leaking, and he wanted to tell a responsible public group the full story.

(McDonald has given several interviews, to The New York Times, NBC News and the Ogden (Utah) Standard-Examiner the past two days detailing his role in the launch decision.)

The four leading senators on the committee which oversees the space program agreed that McDonald should come to Washington for a private session. Hollings and Riegle wanted the session open but eventually agreed at least to get McDonald's story on the record.

But before the engineer could leave his Utah home, he called Hollings to say he needed to bring his superiors from Thiokol. Then he called again asking if a lawyer could come. That was fine. Hollings said he called the commission to let it know of the private session to be held on the Hill.

At some time between Wednesday morning and McDonald's arrival at the senators' meeting, the commission officially invited him to testify, to tell his whole story in a public session on Tuesday of the following week.

Although versions of yesterday's events differ, most sources agree that when McDonald arrived in Washington he was startled to find that the private meeting on the Hill would not be quite so private, that the meeting was generally known about, and that reporters and cameramen were likely to stake out the meeting room.

From the viewpoint of the commission, according to sources, the sequence of events looked like an attempt to steal some of its thunder.

Sen. John C. Danforth (R-Mo.), chairman of the oversight committee, met the engineer when he arrived and arranged for McDonald to avoid reporters and photographers, as well as senators, by secreting him in another room and having him speak to the senators over telephone. But the conversation never got past the subject of whether the meeting should or should not take place.