At least three in five Virginia schools failed to meet annual benchmarks under the federal No Child Left Behind law, a dramatic increase in the failure rate that education leaders attribute to “arbitrary” rules that “misidentify” schools, state officials said Thursday.

Sixty-two percent of Virginia’s public schools fell short of testing goals in math and reading, compared with 39 percent the year before, according to results released Thursday. All but four of the state’s 132 school divisions, including all of those in Northern Virginia, also failed.

The exploding failure rate comes despite a decade of steady academic gains and overall passing rates close to or exceeding 90 percent statewide and throughout much of Northern Virginia.

But under NCLB, the target passing rates for standardized tests increase each year in an effort to meet the federal law’s goal of 100 percent proficiency in reading and math by 2013. Each subgroup of students based on race or disability status or poverty must also meet the same benchmark.

“While this is a laudable goal — one we must continue to strive toward — it is not a basis for a workable accountability system,” Patricia I. Wright, Virginia’s superintendent of public instruction, said in a statement.

In Prince William County, the portion of schools that failed to meet testing benchmarks soared from 34 percent to 75 percent in the past year. And in Loudoun County, it grew from 34 to 57 percent. Fairfax County school officials declined to cite for publication the number of schools that failed to meet the testing goals, referred to as Adequate Yearly Progress.

“This AYP thing has really lost its validity,” said Paul Regnier, a spokesman for Fairfax County public schools. A review of state data shows that half fell short.

Among those schools in Fairfax that now carry a “failing” label is Rachel Carson Middle School in Herndon, an academic powerhouse near the high-tech Dulles Corridor.

“It’s bewildering to me — 180 degrees from what I would expect,” said Tami Holsten, whose daughter is a rising eighth-grader at Rachel Carson and whose son was one of more than 60 Carson graduates to be admitted to the intensely competitive Thomas Jefferson High School for Science and Technology as a freshman last year.

This year, for a Virginia school to succeed, at least 86 percent of students had to show proficiency on state reading tests, and 85 percent had to pass state math tests. That’s an increase from 81 and 79 percent respectively, from the year before.

Rachel Carson had an overall passing rate of 98 percent in English and 95 percent in math, but math scores for black students, Hispanic students, and students from low-income families were lower.

The sharp increase in the portion of schools being classified as failing was prophesied by Education Secretary Arne Duncan in March when he urged Congress to update the 2002 federal education law. Those efforts stalled, and Duncan, exercising his executive authority, announced Monday that he would allow states to apply for relief from the sanctions placed on schools that are labeled as failing.

Wright said she will recommend that the Virginia Board of Education apply for a legal waiver, which is intended to give the state time to set up a new accountability system that would be based on how much students learn throughout the year, not just whether they pass or fail a test on one day.

In Maryland, 44 percent of elementary and middle schools were labeled as failing this summer. And in the District, 87 percent of the 187 public charter and traditional public schools fell short of benchmarks.

Each state gives different standardized tests and can determine different passing rates that schools need to achieve to succeed under the federal law. Virginia prides itself on holding itself to higher academic standards.

“Our schools are continuing to rise to the challenge, but that challenge keeps getting more difficult,” said Jennifer Cassata, director of accountability for Prince William County public schools. “We look at multiple measures for success. And we know these are not failing schools.”

One area where many Virginia districts saw a drop in performance this year was for students with disabilities. Statewide passing rates in English dropped from 73 to 67 percent; passing rates for math dropped from 73 to 66 percent. Prince William and Loudoun counties and the City of Alexandria all had similar declines.

State and local officials said one reason for the drop in scores was the phasing out of a more flexible, alternative portfolio-style test that state lawmakers said was being overused and artificially inflating test scores.

A new computer test will be introduced over the next two years in math and reading that is intended to help students with disabilities who struggle to show what they have learned on a typical test.