Sonar soundings indicate that one of the solid rocket boosters from the space shuttle Challenger may have been found off the Florida coast, space agency officials announced today.

Hopes soared that it would turn out to be the right-hand booster, which flared abnormally before Challenger exploded Jan. 28 and has come to be a chief suspect in the tragedy.

After the explosion, the National Aeronautics and Space Administration announced that the boosters had been destroyed by radio command because it was feared they were veering back toward land, leading to suggestions that they would be so disintegrated as to be useless in the investigation.

Today, a NASA spokesman said that the solid rocket boosters' destructive system does not totally destroy the rockets. "The SRB destructive system slices off the top and the bottom of the rocket, and that stops the thrust," said spokesman Hugh Harris. "Then you have flames spewing out both ends, and it falls straight down. They're awfully large steel casings," and he said it could be assumed that they might be found largely intact.

In a normal shuttle flight, the boosters parachute back to Earth for ocean recovery. Even when the chutes have failed to work on past missions, the sturdily built casings have survived free fall from great heights without disintegrating.

"It would be a miracle, an answer to prayers if it was the right-hand SRB" found by the sonar, said Jim Mizell, a veteran NASA engineer and spokesman.

"We would have actual physical evidence in hand and could check any abnormal burn pattern and even go back and check maintenance. For example, were the bolts torqued properly? We could correlate the data and check against quality control records," Mizell said.

Announcement of the apparent discovery came from NASA's interim review board at 4:30 p.m., shortly after reporters made inquiries based on suspicions voiced in Washington that NASA was keeping a significant discovery under wraps.

Rep. George E. Brown Jr. (D-Calif.), a member of the House Science and Technology Committee, told The Washington Post that he believed search teams already had "a sonar location" for what they think is one of the boosters and, "by now, may even have actually recovered it."

"But I think they're going to keep it secret," Brown said. "They're going to have the situation pretty well under control before they tell you or me."

Asked for comment, NASA officials responded about an hour later with a terse announcement that the "interim review board has confirmed that sonar soundings indicate a solid rocket booster may have been located."

NASA spokesmen said they had not been told the precise location or depth at which the booster may lie. Nor did the agency describe what is being done to recover the rocket.

The boosters broke loose from the disintegrating shuttle system and flew crazily onward until an Air Force range safety officer terminated their flight with an electronic signal after the disaster.

Meanwhile, the search for surface debris entered its final stages, with fewer ships and aircraft at the task. The Coast Guard said the area has shrunk to a 12,500-square-mile area, from New Smyrna Beach north to Charleston, S.C.

Coast Guard spokesmen said the searchers had covered 60,000 square miles in the past week. They recovered more than 12 tons of floating wreckage from the shuttle, which at liftoff weighed 2,300 tons, most of which was fuel.

In recent days, however, fewer and fewer remnants of the shuttle have been found. "The last few days have turned up very little material -- there's been a dramatic dropoff," said Coast Guard Lt. Cmdr. James Simpson. Other Coast Guard officials estimated the surface search has cost $3 million.

So far, there is no confirmation that any human remains have been found, despite recurring rumors to that effect. NASA tonight denied a CBS report that the crew compartment had been found. A spokesman declined to comment on similar reports that personal effects and human remains had been found, citing a policy of not discussing those matters out of respect for the families of the crew members.

[The presidential commission on the Challenger explosion will meet for the first time Thursday in Washington to map strategy. The chairman is former secretary of state William P. Rogers and, The Chicago Tribune reported, his law firm represents the Lockheed Corp., a shuttle contractor, on several matters unrelated to the space program. Rogers told the newspaper, "If any problem arises, I'll recuse myself; I won't vote on anything involving Lockheed."]

Meanwhile, additional questions were raised about whether the low temperatures at Cape Canaveral in the days and hours preceding the launch might be a factor in the disaster. Officials of Morton Thiokol Inc., which makes the boosters, said that the booster fuel is not designed to dip below 40 degrees on the pad before launch. The temperature at the Cape was in the 20s and 30s.

Gilbert Moore, a Thiokol spokesman, said that extremely low temperatures could produce cracks and other irregularities in the fuel that might make it unsuitable for use. However, he said the fuel was well insulated and changed temperature very slowly.

Sources have said that Rockwell International, one of the project contractors, also had weather-related concerns and at least one of its officials advised NASA not to launch Jan. 28 because of icing conditions. NASA spokesmen have repeatedly declined to confirm or deny that report.