The Obama administration granted Maryland and seven other states waivers from the most onerous requirements of No Child Left Behind, the main federal education law, but declined Tuesday to approve similar requests from Virginia and the District.

That means 19 states will no longer have to abide by the law’s toughest requirements, including that schools prepare every student to be proficient in math and reading by 2014 or risk escalating sanctions.

Education Secretary Arne Duncan said Virginia, the District and 16 other applicants can still win approval.

“We’re still working with everybody,” Duncan said. “These were [eight] applications that were further ahead and were absolutely ready. But this is a rolling process, and we’ll keep going. We hope to have another round of announcements in a few weeks.”

In addition to Maryland, federal officials granted waivers Tuesday to Connecticut, Delaware, Louisiana, New York, North Carolina, Ohio and Rhode Island.

The Obama administration issued the first batch of waivers to 11 states earlier this year in response to complaints from teachers and school administrators across the country that the nation’s main education law is outdated and punitive.

Duncan said states are getting waivers because Congress has failed to revamp the 10-year-old law despite broad agreement on Capitol Hill that it is in need of an overhaul.

“We’re thrilled,” said Bill Reinhard, a spokesman for the Maryland State Department of Education. “This gives us some realistic targets when it comes to proficiency and allows us to remove some of the unfair branding of some schools.”

About one of every five public schools in Maryland is considered “failing” under No Child Left Behind — a damaging characterization, Reinhard said.

“Many of these schools are terrific but may have some trouble in one area or another with some students,” he said. “These schools would have gotten a scarlet letter when they didn’t deserve anything like that.”

Under the waiver, Maryland will no longer have to show that 100 percent of students tested are proficient in math and reading by 2014. Instead, schools will have until 2017 to cut in half the number of students who are not proficient. Maryland will also have greater freedom to determine whether schools are progressing toward that goal and what kind of action to take if a school isn’t improving quickly enough.

In addition, the waiver will allow Maryland more freedom in the use of federal dollars to educate poor children. Under No Child Left Behind, the state was required to spend a portion of such money on tutoring, whether or not it led to better results for students, Reinhard said.

“A lot of the tutoring programs were not successful, and we never felt it was a good idea to spend money where our studies showed us it wasn’t working,” he said.

In exchange for relief, the administration is requiring states to 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 communities.

In April, federal education officials wrote to Virginia and the District, detailing concerns about their waiver applications.

They told Virginia to create a more rigorous accountability system, expressed concern about the way Virginia planned to calculate high school graduation rates and said the state’s strategy did not do enough to hold school systems accountable for the performance of subgroups such as poor students, those learning English and racial minorities.

In their critique of the District’s request, federal officials said they were concerned by the city’s history of mishandling federal grants and its troubled record of compliance with special education laws. The officials also voiced concern about how the Office of the State Superintendent of Education — the District’s version of a state education department — will hold accountable the city’s 53 public charter schools.

Virginia and the District tweaked their plans and resubmitted their requests in the past week.

Charles Pyle, a spokesman for the Virginia Department of Education, said the changes Virginia has made are in line with accountability systems in states that have received waivers.

Congress has been trying to rewrite No Child Left Behind for five years, but lawmakers have been unable to agree on the appropriate role of the federal government in local education.

“We prefer a bipartisan rewrite of No Child Left Behind,” Duncan said. “Obviously, that’s not where Congress is right now. . . . Children can’t wait. Teachers can’t wait. We’re moving forward right now.”