The Obama administration is freeing 10 states from the requirements of No Child Left Behind, responding to complaints from teachers and school administrators across the country that the nation’s main education law is outdated and punitive.

“We’ve offered every state the same deal,” President Obama told educators gathered at the White House on Thursday. “We’ve said: ‘If you’re willing to set higher, more honest standards than the ones that were set by No Child Left Behind, then we’re going to give you the flexibility to meet those standards. We want high standards, and we’ll give you flexibility in return.’ We combine greater freedom with greater accountability. Because what might work in Minnesota may not work in Kentucky, but every student should have the same opportunity to reach their potential.”

Obama said he was awarding waivers because Congress had failed to revamp the 10-year-old law, despite broad, bipartisan agreement on Capitol Hill that it is in need of an overhaul.

The waivers will free the states from some of the law’s toughest requirements, including that schools prepare every student to be proficient in math and reading by 2014 or risk escalating sanctions.

In exchange for relief, the administration is requiring a quid pro quo: States must adopt changes that include meaningful teacher and principal evaluation systems, make sure all students are ready for college or careers, upgrade academic standards and lift up their lowest-performing schools. Historically, the federal government has left such decisions to states and local communities.

Lawmakers have been trying to rewrite the law for five years, but they have been unable to come to consensus on the appropriate role of the federal government in local education. A Senate committee approved a bill last year with bipartisan backing, but in the House, Republicans and Democrats are divided.

On Thursday, Rep. John Kline (R-Minn.), chairman of the House Committee on Education and the Workforce, accused Education Secretary Arne Duncan and Obama of usurping the role of Congress. Kline released the final bills in a series of five proposals to replace No Child Left Behind. Only one, aimed at expanding charter schools, has attracted Democratic support.

“Rather than work with us to get it changed, he [Duncan] and the president decided to issue waivers in exchange for states adopting policies that he wants them to have,” Kline told a gathering at the American Enterprise Institute. “. . . This notion that Congress is sort of an impediment to be bypassed, I find very, very troubling in many, many ways.”

Still, several Republican governors celebrated Thursday’s announcement.

“This is not about Democrats or Republicans,” said Gov. Chris Christie (R) of New Jersey, which received a waiver. “It’s about pursuing an agenda in the best interest of our children whose educational needs are not being met and those who are getting a decent education but deserve a great one.”

Joining New Jersey are Colorado, Florida, Georgia, Indiana, Kentucky, Massachusetts, Minnesota, Oklahoma and Tennessee. New Mexico was the only state to apply and not receive a waiver, and Duncan said the state was continuing to work on its application and approval is likely to be forthcoming.

Florida, Georgia and Oklahoma need action by their state legislatures or boards of education, Duncan said, or their waivers will be revoked.

An additional 28 states, including Virginia and Maryland, as well as the District of Columbia, have indicated that they intend to apply this month for a second round of waivers.

After states applied for waivers, their plans were read by peer reviewers, and the administration suggested changes.

“There’s a huge gap between what the states asked for and what they ended up with,” said Michael J. Petrilli of the Thomas B. Fordham Institute, a conservative think tank. “The states asked for a mile, and the administration is giving them an inch.”

But some said the administration might be giving too much leeway. Amy Wilkins of the Education Trust, an advocacy group that seeks to close the achievement gap, said she is concerned that plans submitted by Indiana and Oklahoma don’t do enough to hold schools accountable for educating Latino, African American and other minority children.

When Congress passed No Child Left Behind in 2001, it was a bipartisan effort to hold schools accountable to parents and taxpayers and a federal commitment to attack student achievement gaps.

For the first time, the law required schools to test all children annually in grades 3 through 8 and at least once in high school and report results by subgroups — including race, English learners and students with disabilities — so it was clear how every student was faring.

But administrators and teachers complained that the law unfairly labeled schools as “failures” if just one subgroup failed to meet annual goals and that it focused too much attention a single high-stakes test as opposed to student academic growth over the school year.

According to the Center on Education Policy, 48 percent of the nation’s schools were “failures” last year under No Child Left Behind.

States that receive waivers will still test students annually, but in September, their schools will no longer face the punitive measures outlined in No Child Left Behind, such as firing half a school’s staff members, removing the principal or even shutting down a school altogether.