With his declaration on Friday that he would waive the most contentious provisions of a federal education law, President Obama effectively rerouted the nation’s education history after a turbulent decade of overwhelming federal influence.

Mr. Obama invited states to reclaim the power to design their own school accountability and improvement systems, upending the centerpiece of the Bush-era No Child Left Behind law, a requirement that all students be proficient in math and reading by 2014.

“This does not mean that states will be able to lower their standards or escape accountability,” the president said. “If states want more flexibility, they’re going to have to set higher standards, more honest standards that prove they’re serious about meeting them.”

But experts said it was a measure of how profoundly the law had reshaped America’s public school culture that even in states that accept the administration’s offer to pursue a new agenda, the law’s legacy will live on in classrooms, where educators’ work will continue to emphasize its major themes, like narrowing student achievement gaps, and its tactics, like using standardized tests to measure educators’ performance.

In a White House speech, Mr. Obama said states that adopted new higher standards, pledged to overhaul their lowest-performing schools and revamped their teacher evaluation systems should apply for waivers of 10 central provisions of the No Child law, including its 2014 proficiency deadline. The administration was forced to act, Mr. Obama said, because partisan gridlock kept Congress from updating the law.

“Given that Congress cannot act, I am acting,” Mr. Obama said. “Starting today, we’ll be giving states more flexibility.”