''I'll fight any attempt to do that,'' Bush said at North Glen Elementary School here. ''I'm just not going to let it happen. We're making too much progress.''

The president was evidently alluding to amendments to the law introduced by Maine's two senators, Susan Collins and Olympia Snowe, both Republicans, that the senators say would make the law less onerous for local school districts.

More broadly, many educational groups as well as school boards, state legislators and teachers' unions have called for an overhaul of the law because they say it has grown unwieldy and incomprehensible, and describes many schools as failing when they are not.

Since 2002, the law has required that tests be given annually to children in third through eighth grades and once in high school.

Bush made his comments on the fourth anniversary of his signing of the act and said he had singled out as a backdrop North Glen, a school that has a large number of black students, because of its achievements under the law, which was aimed largely at helping disadvantaged minority students.

In 2003, Bush said, tests showed that 57 percent of North Glen students were proficient in reading and 46 percent were proficient in math. In 2005, he said, 82 percent were proficient in reading and 84 percent in math.

''It's great news, isn't it?'' Bush said.

As for national results, Bush said that in 2005, ''America's fourth-graders posted the best scores in reading and math in the history of the test.''

But some educators said that Bush was selectively citing statistics to bolster his point of view and that a nationwide test administered in 2005 showed the law had achieved mixed results.