School leaders in Virginia and Maryland said they are likely to seek exemptions for the most stringent requirements of the federal No Child Left Behind law after an announcement Monday that the Obama administration will offer flexibility to states willing to modernize their accountability systems.

Education Secretary Arne Duncan is exercising rarely used executive authority by inviting states to apply for legal waivers. The move comes after efforts to update the federal law stalled in Congress this year, frustrating educators across the country.

“I applaud the secretary for recognizing that relief is necessary” said Patricia L. Wright, Virginia’s superintendent of public instruction

Teachers and politicians alike say the law, which sets a goal that all students will perform at grade level by 2014, is outdated and unrealistic. As the deadline approaches, the number of schools failing to meet ever-growing performance goals has gotten higher.

Virginia’s official test results from spring 2011 will not be released until Thursday, but Wright said that the number of schools that missed the mark has increased. Last year, 39 percent of schools were classified as “failing.”

That means that the most troubled schools will be required to offer private tutoring, permit students to transfer or completely overhaul the staff and instructional approaches. Many educators have argued that these solutions aren’t always the right prescription for troubled schools, and have pushed for more freedom to use different strategies.

In Maryland, 44 percent of elementary and middle schools were labeled failing this summer.

“The law needs to be rewritten. Everyone seems to agree, but no one seems to be doing it,” said Bill Reinhard, spokesman for the Maryland Department of Education. He called Duncan’s solution “a step in the right direction.”

A spokeswoman for the office that oversees District of Columbia schools said they are still evaluating the Education Department’s proposal. This year, 87 percent of the 187 charter and traditional public schools in the District failed to meet testing goals in at least one subject.

States will be able to apply for waivers in the fall, but they would not avoid any federal sanctions until after the next round of standardized tests in spring 2012.

The waivers are meant to give states enough freedom to roll out changes to their accountability systems, said Education Department spokesman Justin Hamilton.

More details will be released in September, but Duncan said that waivers would most likely go to states that are aggressively reforming the worst-performing schools and creating tougher academic standards and teacher evaluation systems.

The Obama administration also wants to help states that are implementing modern data systems that measure progress from the beginning of the year to the end, rather than how a student performs on one day, Duncan said.

“No Child Left Behind is focused on proficiency rates; we’re more interested in gains,” Duncan said in a phone call with reporters.

Virginia, Maryland and the District are all pursuing changes in these areas that should make them competitive for federal waivers. Each of the jurisdictions is developing systems that measure growth in student performance as well as more stringent teacher evaluations. The District already uses these scores in evaluations for reading and math teachers in 4th through 8th grades.

Virginia is rolling out more rigorous state math tests this year and tougher reading tests the following year. And Maryland and the District have signed on to a national effort to strengthen their academic standards to dovetail with skills that colleges and workplaces are looking for.

Gene Wilhoit, executive director of the Council of Chief State School Officers, which represents school leaders nationwide, said that Duncan showed “strong leadership” by making way for these improvements rather than standing by while lawmakers debate. “We need some direct action now,” he said.

Staff writer Bill Turque contributed to this report.