CAPE CANAVERAL, Fla. -- NASA officials, increasingly confident they can identify the cause of Challenger's disaster and fly again soon, believe a rupture in the right rocket booster may have triggered the explosion that destroyed the shuttle and killed its crew.

NASA sources apparently feel so close to a solution to Tuesday's tragedy that they are talking about flying again as early as June if the testing and correction procedures are completed.

A flight that had been scheduled by the shuttle Columbia for June 24 appeared to be the earliest possible.

Search teams, fighting strong Atlantic currents, continued to bring in Challenger's spreading debris yesterday, including a five-ton rocket fragment. The search area was extended to more than 40,000 square miles.

"We're finding a lot of empty ocean today," said Lt. Cmdr. James Simpson, a Coast Guard spokesman.

The apparent rupture in the strong rocket casing--whether at a seam or elsewhere--had the effect of pointing a torch at the side of Challenger's fuel tank. The theory is that the flame either burnt through the tank or a "destruct package," causing the explosion, or raised the tank pressure to intolerable limits with the same result.

This theory remained just that. NASA's acting administrator, William Graham, the only agency official speaking on the record, said yesterday that the agency still is looking for other causes for the explosion.

Photographs released by NASA show a tongue of flame apparently lashing upward from the exhaust of the right booster rocket into an area that films of previous launches showed to be clear of fire or flame. The flame appeared in the last 15 seconds of flight.

The flame was "somewhere in this vicinity," Graham said as he made the rounds of television talk shows yesterday.

He pointed to a "field joint"--the seam between the lowest segment of the right booster and the second segment. The name comes form the fact that the segments arrive here individually and are put together at the center.

"We haven't yet finished the analysis and measurements on film to identify the exact point at which the plume [of flame] appeared," Graham said on CBS' "Face the Nation." On NBC's "Meet the Press," he said "we haven't done the measurements yet to see whether it was at the seam or near the seam."

There has been published speculation, based on unidentified sources, that the finger of flame either burned through the fuel tank wall and ignited its huge supply of liquid hydrogen, or that it set off the destruction mechanism by lighting a primer cord.

Graham, asked how soon shuttle flights might resume, replied that there was "no way to say what time we can go forward."

But he added, "This is a fundamentally sound system. It's gone through 24 successful flights. There was obviously an accident. There is a problem there. But the overall configuraion and design, we believe to be fundamentally sound and we believe it won't take a very long time to get this problem corrected."

Rocket Danger Downplayed

For the first 20 years of the space age, solid rockets were considered too risky to use on manned flights. But they proved so successful early in the shuttle program that NASA confidently removed all but four sensors to measure their performance.

But the booster, which NASA officials are now saying may have caused Tuesday's disaster, nearly caused a disaster during the eight shuttle mission in October 1983 as well.

Astronaut Dan Brandenstein reported that a nozzle on a motor came within a fifth of an inch of burning through. Had it burned through, he said, the result would have been "catastrophic," with the craft going into a pinwheeling motion. He believed the five astronauts on board would have been killed.

Graham said yesterday that the boosters were at first heavily instrumented to monitor their performance. But he said the rockets worked so successfully that there were "no credible failure modes that we could identify" and most of the sensors were removed early in the program.

Only four sensors remained on the boosters used for Challenger, and officials said there was no data monitored during liftoff at Mission Control to indicate a problem.