At least 36 public schools in Northern Virginia fell short of full state accreditation this year, up from 14 last year, a consequence of tougher academic standards and state tests that have been introduced in recent years.

Thirteen schools in Fairfax County and nine in Loudoun County failed to meet the basic academic threshold set by the state, compared with just two in each district last year. Prince William County had four schools on the list, up from three last year, and in Alexandria, the number of schools not fully accredited grew from four to six.

Jefferson-Houston School in Alexandria was the only school in Northern Virginia and one of six in the state whose accreditation was denied.

See the list of schools that fell short of full accreditation here.

The trend was mirrored statewide, with just 77 percent of Virginia’s public schools fully accredited, down from 93 percent last year. The number of schools rated “accredited with warning” — indicative of students missing testing goals in one or more subjects — nearly quadrupled to 395.

Virginia education officials emphasized that the new state tests are much more challenging and that the lower ratings don’t mean that schools are performing worse. New math, reading and science tests introduced over the past two years include more critical-thinking and problem-solving skills, designed to better prepare students for college and careers.

“It’s fair to say the floor has been elevated,” David Foster, president of Virginia’s Board of Education, said in an interview. But he emphasized that the new testing goals are still “a floor and not a ceiling.”

“We would like to see more and more students passing these minimum standards,” he said.

School districts across the country are seeing — or expect to see — test scores sink in coming years as they move to align their tests with a national approach to academic standards known as the Common Core.

Virginia is one of a few states that has not adopted the Common Core but independently revised its learning standards and assessments.

For Virginia schools to be fully accredited, at least 75 percent of students must pass the reading and writing Standards of Learning tests, and 70 percent must pass state tests in math, science and history. High schools must also meet a target graduation rate.

On the previous tests, the reading and writing benchmark for middle and high schools was 70 percent. And for the third grade, only half of students had to pass the science and history tests previously.

John Torre, a spokesman for Fairfax schools, said temporary declines in pass rates are expected when academic standards are elevated. But math scores improved in the second year after the new test was introduced, he said, and officials expect to see a turnaround in reading, writing and science as well.

Historically, falling short of full accreditation has triggered state reviews and various levels of intervention, including hiring instructional coaches or turnaround partners.

In the future, accreditation status could be used in some new ways, based on laws passed by the General Assembly last year.

The ratings are likely to be a factor in the A to F letter grades for public schools that the school board has been tasked with developing this fall, Foster said.

Schools that are denied accreditation or accredited with warning for three years — a category that includes 19 schools, none of them in Northern Virginia — could be subject to a takeover by a state-level school board.

The so-called Opportunity Educational Institution could take control of the schools at the end of this school year and convert them to charter schools or college laboratory schools.

The status of the state board remains uncertain, however. The Virginia School Boards Association, along with the Norfolk School Board, filed a lawsuit this month in Norfolk Circuit Court challenging the constitutionality of the law. Attorney General Ken Cuccinelli II (R) declined to defend the case.

“The Virginia Constitution states — and the courts have affirmed — that the supervision of public schools must remain with their local school districts,” said Cuccinelli’s spokesman, Brian J. Gottstein.

J. Tucker Carlson, spokesman for Gov. Robert F. McDonnell (R), who championed the law, said the governor is obtaining outside counsel to defend it.

At Jefferson-Houston, scores improved in three subjects but dropped on the new reading test. Overall, the school still fell far short of the necessary benchmarks to earn accreditation.

Natalie Mitchell, director of Title I programs for Alexandria City Schools, said the school will continue to carry out the changes it has put in place this year as it tries to reach state goals.