"The president believes the comments were not appropriate," White House press secretary Scott McClellan said.
Senate Minority Leader Harry Reid and other Democrats demanded an apology Thursday.
Bennett, on his radio show, "Morning in America," was answering a caller's question when he took issue with the hypothesis put forth in a recent book that one reason crime is down is that abortion is up.
"But I do know that it's true that if you wanted to reduce crime, you could, if that were your sole purpose, you could abort every black baby in this country, and your crime rate would go down," said Bennett, author of "The Book of Virtues."
Listen to Bennett's comments.
He went on to call that "an impossible, ridiculous and morally reprehensible thing to do, but your crime rate would go down. So these far-out, these far-reaching, extensive extrapolations are, I think, tricky."
Responding later to criticism, Bennett said his comments had been mischaracterized and that his point was that the idea of supporting abortion to reduce crime was "morally reprehensible."
Bennett was education secretary under President Reagan and director of drug control policy when Bush's father was president.
Wade Henderson, the executive director of the Leadership Conference on Civil Rights, said Bennett's remarks were "outrageous," and that while an apology by Bennett is appropriate in this situation, it is not sufficient.
Bennett's radio program should be pulled, Henderson told CBS Radio News.
CBS News correspondent Wyatt Andrews reports that for African-Americans, the timing also hurt – right after Katrina, when early reports of a New Orleans crime wave, again by blacks, turned out to be exaggerated.
"I think African-Americans are certainly tired of being stereotyped as being responsible for the majority of crime in American society when the facts simply don't bear that assumption out," Henderson said.
Reid a Democrat from Nevada, said he was "appalled by Mr. Bennett's remarks" and demanded that he "issue an immediate apology not only to African-Americans but to the nation."