The stagnation is "unacceptable," said David Driscoll, chairman of the National Assessment Governing Board, which sets policy for the exam.
"Achievement at this very critical point in a student's life must be improved to ensure success after high school," Driscoll said.
The results follow on just-released research that U.S. high school graduation rates in 2012 reached 80 percent, a record.
John Easton, acting commissioner of the Education's Department's National Center for Education Statistics, said one hypothesis is that lower-performing students who in the past would have dropped out were in the sampling of students who took the exam.
In reading, 38 percent share of students performing at or above proficient was lower than when the assessment was first given in 1992, when it was 40 percent. Scores have remained similar since 1994.
Past comparisons in math date only to 2005. Scores increased from 2005 to 2009, but then stagnated.
The student participants' response to a survey about their educational experiences offers some clues to their performance.
Among the findings:
• Students who reported rarely or never discussing reading interpretations in class had average scores lower than those who did daily or almost daily.
• An overwhelming majority reported that reading is enjoyable. Students who strongly disagreed with the idea that reading is enjoyable had an average score much lower than those who strongly agreed.
• Math scores were higher, on average, for students who took calculus and lowest for students who had not taken a math course passed Algebra I.
• Math scores were higher for students who reported math was their favorite subject, believed the subject would help them in the future or thought their class was engaging.
Even as 12th-grade scores have flat-lined, third- and eighth-grade students have made slow but steady progress on the exam since the early 1990s; most progress came in math. At all levels, there continue to be racial disparities, with white students performing better than African-American and Hispanic students.
Education Secretary Arne Duncan said in a statement that even though there has been some good news related to graduation rates and scores in younger grades, high school achievement has been flat in recent years.
"We must reject educational stagnation in our high schools, and as a nation, we must do better for all students, especially for African-American and Latino students," Duncan said.