Later Wednesday, the House failed to override Mr. Bush's veto. The vote was 235-193 to override, 50 votes short of the two-thirds majority required to send the question to the Senate.
"This bill would support the taking of innocent human life of the hope of finding medical benefits for others. It crosses a moral boundary that our society needs to respect, so I vetoed it," Mr. Bush said.
He explained his decision at a White House ceremony surrounded by 18 families who "adopted" frozen embryos that were not used by other couples, and then used those leftover embryos to have children
"Each of these children was still adopted while still an embryo and has been blessed with a chance to grow, to grow up in a loving family. These boys and girls are not spare parts," he said.
The veto came a day after the Senate defied Mr. Bush and approved the legislation, 63-37, four votes short of the two-thirds margin needed to override.
President Bush didn't want this to be his first veto because a majority of the public disagrees with him on the issue, reports CBS News correspondent Gloria Borger.
Some scientists, and now a majority of Congress, argue that most leftover frozen embryos would not become human life, but could save lives.
"The fact is that there are hundreds of thousands of embryos that are destined to be discarded as medical waste. They could be put to very good use in medical research," Dr. George Daley of Harvard University's Stem Cell Institute tells Borger.
A lot of Republicans voted for this bill, making emotional arguments that this research provides hope to millions of Americans suffering from Parkinson's, diabetes, cancer and other diseases. But backers in the House didn't have the two-thirds majority needed to override this veto.
Mr. Bush has supported federally funded research on only those stem cell lines created before Aug. 9, 2001, the date of his speech to the nation on the subject.
The president vetoed the measure shortly after it came to his desk. His position was politically popular among conservative Republicans, and it was sure to be an issue in the midterm congressional elections.
"Many of the Republicans who voted against the override, but didn't speak on the floor, know that they were wrong," a disappointed Rep. Diana DeGette, D-Colo. said at a press conference after the House vote Wednesday night. DeGette, along with Rep. Mike Castle, R-Del., wrote the Stem Cell Research Enhancement Act (H.R. 810).
"They feel for whatever reason that they can't buck their president," DeGette said of the Republicans.
Announcing the veto, Mr. Bush was surrounded in the East Room by so-called "snowflake" families, those with children born through embryo donation.
"They remind us of what is lost when embryos are destroyed in the name of research. They remind us that we all begin our lives as a small collection of cells. And they remind us that in our zeal for new treatments and cures, America must never abandon our fundamental morals," he said.