Students across the United States have made some gains but continue to lag behind many of their Asian counterparts in reading, math and science, according to the results of two international tests released Tuesday.

U.S. fourth-graders' math and reading scores improved since the last time students took the tests several years ago, while eighth-graders remained stable in math and science. Americans outperformed the international average in all three subjects but remained far behind students in such places as Singapore and Hong Kong, especially in math and science.

Jack Buckley, commissioner of the National Center for Education Statistics, said the results leave him "optimistic" about the United States' performance, particularly given that many other higher-performing nations do not deal with the same wide range of student and family income, backgrounds and language ability.

"We have a large and diverse population of kids to educate, and I think these results show that we're doing pretty well," Buckley told reporters Monday.

Still, the results are likely to fuel concerns among business leaders, policymakers and many educators, who worry that the U.S. will not be able to compete globally if U.S. students cannot keep up academically with their peers around the world.

In fourth-grade math, for example, students in Singapore, South Korea, Hong Kong, Taiwan, Japan, Northern Ireland and the Flemish region of Belgium outperformed U.S. students. Finland, England and Russia also posted higher average scores, but the differences were statistically insignificant.

In eighth-grade science, children in Singapore, Taiwan, South Korea, Japan, Finland, Slovenia, Russia and Hong Kong beat U.S. students.

The results were drawn from the 2011 Progress in International Reading Literacy Study, known as PIRLS, and the Trends in International Mathematics and Science Study, referred to as TIMSS.

The literacy test, which fourth-graders take every five years, was administered to a representative sample of public- and private-school students in 53 countries, states and regions. The math test is taken every four years by fourth- and eighth-graders in more than 55 countries, states and regions.

A handful of U.S. states volunteered to give the tests to their students and be graded as if they were countries, to see how their students perform compared with international benchmarks.

Florida, the only state that volunteered to take the reading exam, emerged as a leading scorer on that test among all countries and states that administered it. Only students in Hong Kong scored higher, but the difference was not significant.

Boston College professor Walter Haney said Florida's scores are misleading because, since 2004, Florida has held back struggling third-grade students who are not reading on grade level, preventing them from advancing to the fourth grade, when the test is taken.

Several states that took the test independently scored higher than the U.S. average in eighth-grade math, including North Carolina, Indiana, Massachusetts and Minnesota.