Paige said later in an interview that his comment was "a bad joke; it was an inappropriate choice of words." President Bush was not present at the time Paige made the remark.
"As one who grew up on the receiving end of insensitive remarks, I should have chosen my words better," said Paige, the first black education secretary.
Democratic Governor Jim Doyle of Wisconsin said Paige's words were, "The NEA is a terrorist organization."
Paige said he had made clear to the governors that he was referring to the Washington-based union organization, not the teachers it represents.
To that, Weaver said, "We are the teachers, there is no distinction."
Catherine A. Boudreau, president of the Massachusetts Teachers Association, the NEA's local affiliate, said: "Paige's remark would have been ignorant and tasteless coming from anyone. Coming from the secretary of education, it is also incredibly reckless and irresponsible."
Paige's Education Department is working to enforce a law that amounts to the biggest change in federal education policy in a generation. He has made no attempt to hide his frustration with the NEA, which has long supported Democratic presidential candidates.
Asked whether he was apologizing, Paige said: "Well, I'm saying that I'm sorry I said it, yeah." In a statement released to the media, Paige said he chose the wrong words to describe "the obstructionist scare tactics" of NEA lobbyists.
White House spokesman Scott McClellan said, "The comment was inappropriate, and the secretary recognized it was inappropriate and quickly apologized."
Terry McAuliffe, chairman of the Democratic National Committee, put it in stronger terms, accusing Paige of resorting "to the most vile and disgusting form of hate speech, comparing those who teach America's children to terrorists."
Education has been a top issue for the governors, who have sought more flexibility from the administration on Bush's No Child Left Behind law, which seeks to improve school performance in part by allowing parents to move their children from poorly performing schools.