A somber President Reagan paid homage yesterday to the "seven heroes" who died aboard the Challenger and vowed that the United States space program would go forward despite the tragedy.

"The future doesn't belong to the fainthearted. It belongs to the brave," Reagan said in a nationally televised speech from the Oval Office. "The Challenger crew was pulling us into the future, and we'll continue to follow them."

Reagan went on television after postponing the State of the Union address that he was supposed to deliver last night before a joint session of Congress. That message, consisting largely of optimistic themes, was put off for a week because of the space shuttle explosion.

"I've always had great faith in and respect for our space program. And what happened today does nothing to diminish it," Reagan said. ". . . We'll continue our quest in space. There will be more shuttle flights and more shuttle crews and yes, more volunteers, more civilians, more teachers in space. Nothing ends here. Our hopes and our journeys continue."

In his speech the president voiced his grief for "the tragedy of the shuttle Challenger" but expressed his confidence in those in charge of the U.S. space program.

" . . . I wish I could talk to every man and woman who works for NASA or who worked on this mission and tell them, 'Your dedication and professionalism have moved and impressed us for decades and we know of your anguish,' " the president said. " 'We share it.' "

White House spokesman Larry Speakes told reporters that he had not heard the president "express any regret" that he had sent the Challenger on its unsuccessful mission.

"Concern, yes; deep emotion, yes; sorrow, yes -- but regret is not that," Speakes said in reaffirming Reagan's support of the program.

Meeting with television reporters for what had been scheduled as a briefing on the State of the Union address, Reagan said the space program had seemed so safe after 56 flights that Americans had "gotten a little impatient when some flights had been aborted and . . . it seems as if they were taking things too seriously.

"Now we know they weren't," Reagan continued. "And so I'm confident that there will be no flight until they are absolutely as certain as a human being can be that it is safe."

In this meeting the president said he did not expect a public backlash against the space program because of the tragedy.

"We have accidents in every line of transportation, and we don't do away with those things," Reagan said. "They've probably got a better safety record in the space program than we have on the highways."

The president, described by aides as somber and silent during much of the day, said "I can't get out of my mind" the husband and children of Christa McAuliffe, the teacher killed yesterday in the Challenger explosion. He had planned to mention her in his State of the Union speech, White House officials said.

In his televised speech Reagan listed the names of the seven members of the crew killed aboard the Challenger and said:

"To the families of the seven, we cannot bear as you do the full impact of this tragedy, but we feel the loss and we're thinking about you so very much. Your loved ones were daring and brave and they had that special grace, that special spirit that says, 'Give me a challenge and I'll meet it with joy.' "

Reagan said that the space program, after 25 years, was still in its infancy even though Americans had grown used to technological wonders.

"We've grown used to the idea of space and perhaps we forget that we've only just begun," Reagan said. "We're still pioneers. They, the members of the Challenger crew, were pioneers."

The speech was drafted by Margaret (Peggy) Noonan, a writer often used by Reagan for the preparation of patriotic or inspirational speeches.

It ended with a comparison of the Challenger mission to the explorations of the English explorer Sir Francis Drake and an emotional tribute to the shuttle crew.

"The crew of the space shuttle Challenger honored us by the manner in which they lived their lives," Reagan said. "We will never forget them nor the last time we saw them -- this morning -- as they prepared for their journey and waved goodbye, and slipped the surly bonds of Earth to touch the face of God."

The concluding words were taken from a poem, "High Flight," by John Gillespie Magee Jr., an American pilot who served with the Royal Canadian Air Force.

At age 19, he died in combat in December 1941.