The space shuttle Challenger, carrying six astronauts and schoolteacher Christa McAuliffe, exploded in a burst of fire 74 seconds after liftoff yesterday, killing all seven aboard and stunning a world made witness to the event by television.

The unexplained explosion occurred without warning as the flight seemed to be proceeding flawlessly at about 2,900 feet per second, 10 miles above Earth and eight miles down range from Cape Canaveral. The spacecraft appeared to disintegrate into bits of debris that rained into the Atlantic Ocean. Those aboard, still strapped into their seats, had no means of escape.

In addition to McAuliffe, those killed were spacecraft commander Francis R. (Dick) Scobee, Navy Cmdr. Michael J. Smith, mission specialist Judith A. Resnick, mission specialist Ronald E. McNair, Air Force Lt. Col. Ellison S. Onizuka, and payload specialist Gregory B. Jarvis.

It was the worst accident in the history of space exploration and the first time anyone has been killed during an American space flight. The tragedy occurred 19 years and one day after U.S. astronauts Virgil I. (Gus) Grissom, Roger A. Chaffee and Edward H. White died during a training session when a fire broke out in their sealed Apollo spacecraft on the launch pad.

Five hours after yesterday's tragedy, Jesse W. Moore, associate administrator for space flight of the National Aeronautics and Space Administration, announced from Cape Canaveral that the shuttle program had been suspended for an exhaustive investigation. But President Reagan, who postponed his State of the Union speech from last night to next Tuesday, vowed in a nationally televised statement from the Oval Office that exploration of space would continue.

"There will be more shuttle flights and more shuttle crews and, yes, more volunteers, more civilians, more teachers in space," Reagan said. "Nancy and I are pained to the core over the tragedy of the shuttle Challenger. We know we share this pain with all of the people of our country. This is truly a national loss."

NASA officials, appearing shaken and bewildered by the fate of the 25th mission in five years of shuttle flights, said they could offer no reason for the accident and declined to speculate on causes.

The accident occurred just before 11:40 a.m. EST. Soon afterward, NASA's normally detailed mission commentary went silent. Not until Moore's brief statement five hours later did space agency officials offer any comments.

"We thought everything was in good shape for a launch this morning," Moore said.

He told reporters that he had appointed an "interim investigating board" that would impound all data on the flight, including technicians' notes, and turn them over to a formal review board to be appointed "in the next day or two" by NASA's acting administrator, William R. Graham.

Graham, along with Vice President Bush, was dispatched by President Reagan to the Kennedy Space Center to begin an investigation. Bush arrived at the Florida cape late in the afternoon and immediately went to comfort relatives of the crew.

Crew members, praised by President Reagan in his televised statement as "seven heroes," were: McAuliffe, 37, a social studies teacher from Concord, N.H., with a degree in education from Bowie State College here. She was chosen last July to be the first teacher in space. Spacecraft commander Scobee, 46, a NASA astronaut from Cle Elum, Wash., who was on his second shuttle flight. Navy Cmdr. Smith, 40, the pilot, an aeronautical engineer from Beaufort, N.C., and a NASA astronaut since 1980, who was on his first shuttle flight. Resnik, 36, the second American woman in space, a mission specialist from Akron, Ohio, with a doctorate in electrical engineering from the University of Maryland, who was on her second shuttle flight. McNair, 35, the second black American in space, a mission specialist from Lake City, S.C., with a doctorate in physics, who was on his second shuttle flight. Air Force Lt. Col. Onizuka, 39, a Hawaiian-born aerospace engineer and astronaut since 1978, who was a mission specialist and crew member on the program's first secret mission for the Defense Department. Jarvis, 41, a Hughes Aircraft Co. electrical engineer from Detroit who was on his first mission as a payload specialist.

McAuliffe's parents, Edward and Grace Corrigan, were watching the flight from the VIP viewing site at the space center. When it was apparent that the fireball was not an expected part of the flight, their faces showed confusion and grief as they hugged each other and sobbed.

McAuliffe's students, who had gathered in Concord High School to watch the launch on television, cheered wildly when the 1.6-million-pound rocket rose from the pad. A minute later, they subsided into stunned silence.

President Reagan had words for the many schoolchildren around the country who were planning to watch McAuliffe teach lessons from orbit. "I know it's hard to understand," Reagan said, "but sometimes painful things happen. It's all part of the process of exploration and discovery. The future doesn't belong to the fainthearted."

Others in official Washington were stunned by the news. Sen. John Glenn (D-Ohio), the first American to orbit the Earth, said he felt a "profound, personal sense of loss." Glenn, noting the success of the program, said, "We hoped we could push this day back forever."

Sen. Jake Garn (R-Utah), who flew aboard the shuttle last April, appeared visibly shaken as he told reporters that "these were my friends. Mike Smith, the pilot, was my mother hen," guiding him through flight training.

Both Glenn and Garn said they would be willing to go up again in space and that they believed the program should go on.

A former defense official, who is knowledgeable about the shuttle and who talked with NASA engineers about yesterday's disaster, speculated that there could have been a failure in the pumps that feed fuel to the shuttle's main engines. The official, who asked not to be named, said he came to his conclusion after viewing NASA videotapes of the explosion.

"Detonation apparently occurred at the base of the orbiter itself the shuttle craft and secondly the two SRBs solid rocket boosters attached to the side of the main fuel tank of the shuttle became disassembled," he said. "They seem to be intact and flying off separately on their own."

If the problem did rest with the main engines, the former official said, "it is 60 to 70 percent certain it was the pumps." He said the pumps operate at extremely high temperatures and pressures and are vulnerable to breaking up. If that happened, a piece of the pump may have been flung out to puncture a fuel tank or a fuel line.

In that case, heat from the shuttle's engines could have ignited the spilling fuel, causing an initial small fire. If this then heated the main fuel tank, it could have ruptured and fed the ensuing fireball.

There was also speculation that the enormous external fuel tank ruptured during ascent, releasing highly volatile liquid hydrogen and oxygen.

The shuttle program had appeared unusually problem-plagued over the last month. The last mission, a flight of Columbia, had been postponed a record seven times before liftoff. That also forced the first of six postponements of the Challenger, which was originally set to lift off Jan. 22.

Challenger's launch was delayed two hours yesterday because of subfreezing temperatures that caused icicles to form on the launch tower. It was feared that the launch would knock them loose and allow them to damage the shuttle as it rose.

When it was determined that the ice would be no danger, the countdown was allowed to proceed. As planned, six seconds before liftoff, fuel from the main external tank, liquid hydrogen and liquid oxygen, flowed into the shuttle's main engines and ignited. Then the two solid fuel rockets, strapped to the side of the main tank, began firing.

When thrust reached maximum, the entire vehicle was released, at 11:38 a.m. EST, to rise from the pad. At full power, it climbed, riding a 700-foot pillar of fire into a cold but cloudless sky. About a minute into the flight, pilot Smith throttled back the main engines to ease the passage through the few seconds in which rocket forces shake and rumble the accelerating vehicle. This period, known as maximum dynamic pressure, is normal.

Once through the critical period, mission controllers gave Smith the go-ahead to throttle up to full power. Smith replied, "Roger. Go at throttle up." Those were his last words.

As NASA tracking cameras recorded it and as millions either saw it live or watched repeated television reruns, a flame appeared to start at the base of the shuttle's main tank, which still contained an estimated 1.2 million pounds of highly volatile fuel, and quickly raced up the side. Less than a second later, flames appeared between the tank and the orbiter, which carried the crew, and almost instantly the entire vehicle was engulfed in a billowing fireball.

As unidentifiably small smoking fragments rained into the ocean, the vehicle's two solid fuel boosters continued firing, rocketing aimlessly out of the fireball.

A recovery mission -- Air Force, Navy and Coast Guard ships, planes and helicopters with rescue divers -- was immediately dispatched to pick up debris and any human remains, but was reportedly delayed from entering the area because of debris, which continued fluttering down over an area 50 by 100 miles for 35 minutes.

Lt. j.g. Rudy Holme, pilot of a Coast Guard search helicopter, said last night that the crew of a Coast Guard C130 cargo plane, which reached the search site about 30 minutes after the explosion, soon "spotted an area in the water that was bubbling . . . . It was obviously the area impacted by the airframe of the Challenger."

Holme said he and his crew then spotted a large piece of debris, 10-by-10 feet, but he said they could not determine what it was. Throughout his nearly nine hours in the air, Holme said, he spotted many bits of debris, some only a few inches long, spread widely over the water. He said the focus of the search, where the bubbling water was spotted initially, was about 37 miles offshore.

Holme said there was no sign of the crew or their belongings. The search flights were scheduled to begin again at first light on Wednesday.

Rep. Bill Nelson (D-Fla.), who flew on the last shuttle mission, said that from his experience, it was unlikely the seven crew members knew anything was wrong or had any chance of survival. Nelson said NASA's preparations for a flight are so thorough that crew members "expect that everything is going to be nominal normal . When there is an explosion such as you had today, there are no contingencies. That is one of the risks."

The only previous serious in-flight space accident on an American mission came during Apollo 13's voyage to the moon in 1970. It ended without injury after an explosion in the service module tank. In 1981 two NASA employees were killed in a preflight ground test of the shuttle.

Four Soviet cosmonauts are known to have died in spaceflight accidents, all during reentry. There have long been rumors of other Soviet space accidents that were kept secret. In October 1983, a Soviet rocket exploded on the pad but the three cosmonauts aboard were ejected and parachuted to safety.

Today's space shuttles have no ejection seats. Such safety features had been incorporated into the early versions of the spacecraft, used in the first four shuttle flights when only two astronauts were aboard. When later flights called for more crew members, the heavy ejection seats were removed to save weight and make room for extra seats.

Preliminary indications suggest that yesterday's accident happened too fast for ejection seats to have been useful.

The Coast Guard in Miami is concentrating its search in a 1,200-square-mile area of the Atlantic, centering on a spot 30 miles southeast of Cape Canaveral.

At least 11 ships, including patrol boats ranging from 41 feet long to the 378-foot cutter Dallas, were searching the area into the night. Ten aircraft, including six helicopters and four two-engine planes, flew until dark.

The only recognizable item reported as spotted was one of the two solid-fuel rockets that flew beyond the fireball, splashing 18 to 20 miles downrange.

Pilots coming back from the search area said that water seemed discolored in spots, and reported seeing widely scattered pieces of debris, according to Coast Guard spokesmen.

While it is unclear how much of the wreckage will eventually be found, NASA has an extensive record of the launch and the short flight, recorded by about 120 cameras, including 60 television cameras and a varied array of movie and still cameras. They shot from many angles, some in extreme closeup on the shuttle's engines and hardware, others in wider-angle shots. Several cameras were mounted on a helicopter flying at a distance from the rising shuttle. The rest were mounted on the ground, and used lenses up to 300 inches long to track the launch.

The video replays that networks repeated all day were provided by NASA from only a few of the cameras. When footage from the others is examined it may be possible to see new details of what happened. All the cameras and film have been impounded for examination by the review board.

Challenger, which cost $1.2 billion and was one of NASA's four shuttles, had been the workhorse of the program, successfully completing nine of the 24 previous shuttle flights.

In preparations for previous missions, Challenger had experienced a number of mishaps. Its maiden flight, in April 1983, was delayed for two months so technicians could repair a faulty fuel line that leaked highly flammable liquid hydrogen. But it performed well after the repair.

Last July, a Challenger countdown was stopped three seconds before liftoff when a heat sensor falsely indicated that one of the three main engines was overheating. That, too, was successfully repaired but when Challenger finally lifted off, later that month, one of the main engines shut down prematurely. The spacecraft, however, had already achieved sufficient speed to make it into orbit.

Yesterday's launch was the second this year of what was to have been NASA's most ambitious year in space. Thirteen more shuttle flights had been scheduled for 1986 but all have been put on an indefinite hold, pending the investigation.

Some critics have argued that NASA was pushing too hard to demonstrate the usefulness of the shuttle program, which has suffered from years of criticism that it was not economically worthwhile.

In addition to McAuliffe's mission to teach from space,, Challenger's crew had planned to observe Halley's comet and launch a communications satellite for NASA.

Moore, the NASA official who briefed reporters after the accident, denied there was any pressure to get this Challenger mission, 51-L, into space.

"Flight safety," Moore said, "is our number one priority in the space shuttle program."