Prince George's County third and fifth graders have scored at or above the 60th percentile on national standardized tests, the highest scores ever registered by county students taking those tests, according to results released yesterday. Black students, who showed the biggest gains, scored above the national average for the first time.

The results of the California Achievement Test, given last fall to third, fifth and eighth graders, represent good news for the school system that, with 104,000 pupils, is second largest in the Washington area.

Prince George's schools have been struggling for years to overcome tight budgets, a lingering desegregation lawsuit and a reputation of being second rate compared to other suburban school systems in the area.

"We feel very encouraged," said Superintendent John A. Murphy, who is in his second school year as the chief administrator. "When I came here I thought this was a school system that could move well beyond the average range."

There was significantly less movement in scores, also released yesterday, on state-mandated math and reading tests required for high school graduation.

On the Maryland Functional Reading test, 90.5 percent of the ninth graders passed, compared with 90.8 percent last year. On the math test, 52 percent of the ninth graders passed, the same rate that passed last year but a drop of 2 points since 1983.

Third graders taking the California Achievement Test this year scored at the 64th percentile, meaning that 64 percent of the third graders tested nationwide did worse. This year's third graders' score was 6 percentile points higher than last year's third graders' score. Fifth graders were up 2 points to the 60th percentile and, at the eighth grade level, students scored in the 58th percentile, 8 points above the national average and 2 points over last year.

Black students, who make up nearly 60 percent of the county's enrollment, showed much higher gains on the California Achievement Test this year than their white counterparts. Black students at the third grade level, for example, improved by 12.5 percent over the previous school year, compared with a 4.1 percent rise for white students.

The gap between the scores of black and white students has become a focal point for all of the area school systems in recent years, and several, including Prince George's County, have targeted programs aimed at reducing it. There is still a gap of more than 20 percentile points in the county, but the gap has narrowed a few points at each grade level over last year.

"White students have always felt comfortable in our schools, and it's always been assumed they would do well," said Sarah Johnson, one of two black members on the county Board of Education. "This year, black students have been included in that perception."

She said the improvement in test scores may be due to a better climate in the school system. "For the first time in a long time, everyone is feeling very good about the system . . . teachers feel the need to do more for children, and that includes black children."

Murphy said the improvement in test scores this year reflects higher expectations placed on students by teachers, a philosophy he has encouraged since he arrived in July 1984. Also, he said the scores stem from a program of "effective schools," implemented during the last year, in which principals and teachers set goals, focus on the performance of individual students and are then held accountable for student achievement.

Paul Pinsky, president of the county's teacher union, said that "teachers are trying to do their all to improve the educational system."

County students scored above the national average in every subject area, measuring the highest in language, with third graders scoring 18 percentile points above the national average in that subject.

Murphy predicted that scores will continue to rise as the impact of academic programs implemented with a magnet school plan this year is felt. He has said he wants the county to be the first school system in the nation with a majority enrollment of minority students to score in the 75th percentile.

"The data in this year's test scores shows that is definitely in our reach," Murphy said.