For years, National Aeronautics and Space Administration officials were "walking right on the edge of a cliff" because they failed to correct flaws in solid-rocket booster joints that led to the fatal space-shuttle explosion Jan. 28, the agency's chief investigator into the disaster said today.

James R. Thompson, vice chairman of the NASA internal task force formed to investigate the accident, said the group has identified four problems involving the joints and that these combined to trigger the explosion in which seven astronauts were killed.

Thompson said the agency probe shows that the joint has "several shortcomings" that should have been fixed and has a "quite marginal" design.

"We were walking right on the edge of a cliff, and several of these factors just pushed us over," Thompson said at a news conference here. "Clearly, we just missed it on this joint. We missed it on the design . . . . Some of the prior flight anomalies just really weren't taken seriously."

The task force is to make a preliminary report Thursday and a final report April 18 to the presidential investigating commission headed by former secretary of state William P. Rogers.

The comments by Thompson, a Princeton University physicist appointed last month to manage the probe, were among the harshest internal criticisms of NASA's failure to correct problems in the rocket joints.

"Nobody feels worse than the people directly involved in the launch," he said. " . . . In the last two months, we have run about 300 tests. I wish some small fraction of those could have been run earlier."

James Kingsbury, director of the Science and Engineering Directorate at NASA's Marshall Space Flight Center in Huntsville, Ala., one of several agency officials responsible for the booster rockets, challenged Thompson's contention that the flaws should have been corrected sooner.

"I did not perceive this joint [as] . . . not flight-worthy," he said. "It had worked for four years and 24 flights before. What we had here [with Challenger] were . . . a new set of conditions that we hadn't experienced before." As a result of the task force's findings, Thompson said NASA must "go back and look at everything and make sure something else isn't winking and setting us up for another problem."

He said this process, which includes redesign of rocket joints and perhaps other components, is likely to take longer than the 12-month timetable set publicly by NASA for resumption of shuttle flight.

Thompson said NASA can say conclusively that the explosion was caused by failure in a single joint of the lower portion of the right solid-rocket booster. The boosters are composed of four segments stacked vertically and sealed at the joints to prevent exhaust gases from escaping during launch. Inside each joint and covering the booster's circumference are two rubbery O-rings designed to make the seals airtight.

Rather than isolating a single defect in the joint, Thompson said, the task force zeroed in on four factors, some combination of which probably produced the black smoke emitted from the joint during the first second of flight.

He said the factors were:

*The known tendency of the rocket's joints to rotate during pressure of liftoff.

*The impact that morning of subfreezing temperatures believed to have caused the O-ring seals to stiffen, hindering their ability to contain hot gases.

*Defects in putty used to protect the O-rings from hot gases inside the boosters.

*Slight damage to a rocket segment during assembly that may have squashed the O-ring, allowing gaps that permitted gas to escape.

Thompson emphasized that some, if not all, of these problems could have been corrected before the fatal flight had NASA officials paid more attention to evidence from previous flights.

Despite the publicly defiant attitude of officials at Marshall Space Flight Center, who ignored warnings about cold weather from rocket engineers on the eve of the launch, Thompson said those and other NASA officials who approved the Challenger launch now "hurt inside."

None of the task force's findings is likely to be altered as further Challenger wreckage is recovered, he said.