The seven died Saturday over Texas when the shuttle broke apart, scattering debris over a huge area and bringing a tragic end to an otherwise successful 16-day scientific mission.
"Today we remember not only one moment of tragedy, but seven lives of great purpose and achievement," Bush said at the outdoor memorial ceremony. "To leave behind Earth and air and gravity is an ancient dream of humanity, and for these seven it was a dream fulfilled.
"Each of them knew that great endeavors are inseparable from great risks. Each of them accepted those risks willingly, even joyfully, in the cause of discovery."
As the first couple stood under a clear sky, the families of the deceased astronauts walked up to them and took places to either side.
A U.S. Navy chorus sang the hymn, "Our God, Our Help in Ages Past," the lyrics of which say in part: "Thy Word commands our flesh to dust, return, ye sons of men: All nations rose from Earth at first, and turn to Earth again."
A U.S. Navy rabbi opened the ceremony, intoning a prayer in Hebrew. NASA Administrator Sean O'Keefe then took the microphone and told thousands of mourners -- NASA employees and contractors in addition to families and guests -- the agency's "unceasing efforts" in exploring space would be a tribute to the fallen.
The agency, he said, would also leave no stone unturned in discovering what caused the shuttle to break up just minutes before it was scheduled to land in Florida and "make sure this never happens again."
Twelve children lost a parent in the disaster. They sat side by side with their families at the service. Some looked down at their hands, while others lay their heads on relatives' shoulders. One young girl sat holding a white teddy bear with a red and blue ribbon around its neck.
A group photograph of the lost crew wearing their orange space suits was perched on an easel on the podium. A ship's bell sat at the right of the podium.
Outside the Kennedy Space Center in Florida, meanwhile, mourners streamed along the walls. They left flowers, notes, cards and other tokens of sympathy at the entrance. Some, wiping tears from their eyes, stared blankly at what had become a massive makeshift memorial.
At the Smithsonian's Air and Space Museum in Washington, officials and dignitaries watched the ceremony on a wide-screen TV as they sat under decades of historical flight memorabilia.
President and Mrs. Bush sat in the front row at the ceremony with their hands folded in their laps. The president appeared to lean slightly towards his wife, as if seeking support for what was obviously an emotional moment for a president who has had more than his fair share of national tragedy since taking office.
Navy Capt. Kent Rominger, chief of the astronauts' office of NASA, spoke movingly of each of the deceased, relating humorous stories about them and highlighting their dedication to exploration.
Bush followed suit. "The final days of their own lives were spent looking down upon this Earth, and now on every continent, in every land they could see, the names of these astronauts are known and remembered," Bush said.
"They will always have an honored place in this country. And today, I offer the respect and gratitude of the people of the United States."
Bush noted their loss would be painful for the families but said they were not alone in their grief. America mourned with them.
"The families here today shared in the courage of those they loved," he said. "But now they must face life and grief without them. The sorrow is lonely; but you are not alone. In time, you will find comfort and the grace to see you through. And in God's own time, we can pray that the day of your reunion will come."
Shuttle Columbia was the oldest craft in NASA's fleet of space vehicles. Investigators are focused on its left wing where flying debris during take-off might have caused damage.
NASA has discovered that the area at the back of the wing, and a section of the fuselage above the left wing, were overheating just before sensors went out and the shuttle disintegrated at an altitude of more than 200,000 feet and at a speed of more than 12,000 miles per hour.
Thousands of those pieces were scattered over Texas and part of Louisiana.
NASA and Bush have repeatedly said the space program would go forward.
The last fatality for the U.S. space program was in 1986, when seven astronauts died aboard the Challenger as it exploded on take-off.
The simple but moving ceremony ended with a reading of Psalm 23, with the rabbi reading first in Hebrew, and another Navy chaplain then reciting the English-language version.
NASA astronauts flew T-38 jet trainers over the complex in the missing-man formation. And seven peals from a ship's bell were also sounded -- one for each of the lost crew.
Bush met privately for about 40 minutes with the families following the ceremony in a large room at the facility. He sat with them, put his arm around them and kidded a bit with the children present.
"I'm sorry we meet under these circumstances," an official quoted Bush. "God bless you all. He has blessed you," Bush said.