Grief, investigations and soul-searching shrouded America's troubled shuttle program Tuesday after the catastrophic explosion of Challenger that took seven lives -- the greatest tragedy in man's conquest of space.

''We mourn seven heroes,'' said President Reagan.

As students around the nation watched on television, schoolteacher Christa McAuliffe and six astronauts perished in a huge fireball when it was 10 miles high and 8 miles south-southeast of Cape Canaveral at 11:39 a.m., 75 seconds after launch.

It was the first time American astronauts died in flight, and the worst U.S. space tragedy since Gus Grissom, Ed White and Roger Chafee died in an Apollo spacecraft fire during a mock countdown Jan. 27, 1967.

Victims of America's 56th manned spaceflight, the 25th of the shuttle program and Challenger's 10th were commander Francis ''Dick'' Scobee, 46, pilot Michael Smith, 40, Judith Resnik, 36, Ellison Onizuka, 39, Ronald McNair, 35, engineer Gregory Jarvis, 41, and McAuliffe, 37, the Concord, N.H., social studies teacher chosen from 11,000 applicants to be the first private citizen in space.

Many of their families, including McAuliffe's, watched in horror from nearby sites several miles from refurbished launch pad 39B, used for the first time since 1975.

Hours later, heat-resistant shuttle tiles began washing ashore south of the Cape. Passers-by were taking them to the south gate of the Cape, where they were being driven to the Kennedy Space Center.

Col. Bob Nicholson, an Air Force spokesman, said every available piece of debris would be needed for the investigation. But he said some debris could contain explosives, and for people to call the Air Force if there is any question about the nature of the debris.

Rescue craft were retrieving other debris, mostly tiles.

Stunned NASA officials refused to speculate on what went wrong, but it appeared trouble could have developed in the huge external fuel tank, launched with 528,000 gallons of volatile liquid propellants.

The 2,200-ton spaceplane, whose boosters carried 2.2 million pounds of solid propellant, lifted off normally at 11:38 a.m. Then the boosters ejected sideways as Challenger and the external tank exploded.

The boosters spiraled away, spinning like skyrockets with flames gushing from their nozzles as they careened toward the Atlantic far below.

There was no sign of life.

Television pictures indicated the explosion might have originated in the shuttle's external tank.

''We will not speculate as to the specific cause of the explosion based on that footage,'' said NASA shuttle chief Jesse Moore. ''It will take all the data, a careful review of that data before we can draw any conclusions on this national tragedy.''

He said the space agency is forming an investigating board that will make a ''careful review'' of all data ''before we can reach any conclusions.'' Two congressional committees announced investigations.

Moore said he had created an interim investigative board ''to implement preliminary activities in this tragedy,'' to secure all data so it can be fully analyzed.

NASA acting Administrator William Graham will appoint an official investigation board within a day or two, Moore said.

''Data from all the shuttle instrumentation, photographs, launch pad systems, hardware, cargo, ground support systems and even notes made by any member of the launch team and flight operations team are being impounded for study.''