The state of Virginia, saying it has made "dramatic progress" toward eliminating the remnants of its segregated college system, today asked the federal government to seek an end to its court-supervised 16-year-old desegregation effort.

The surprise action came in a request to the U.S. Department of Education and asked the agency's Office of Civil Rights to seek federal court approval to exempt Virginia from establishing any new desegregation plans after its current one expires next year.

If approved by the agency and a federal judge overseeing desegregation of colleges across the South, the action would be seen as a major achievement for the administration of Virginia Gov. Charles S. Robb. His is the fourth administration that has struggled with the controversy that has threatened to cost the state millions of dollars in federal education funds.

None of the 17 states, including Maryland, that have been involved in the lawsuit over the issue has been successful in removing itself from federal monitoring of college desegregation plans, a Department of Education spokesman said.

"We should be let out from underneath this because of the progress we made," said George M. Stoddart, Robb's press secretary. Stoddart said changes by the Robb administration have "institutionalized" desegregation throughout the state's college system. "It would just take an enormous effort on somebody's behalf to dismantle what we have done," he said.

The Virginia request met with skepticism from attorneys for the NAACP Legal Defense Fund.

The fund had sued federal education officials in the early 1970s over what the NAACP said was lax enforcement of desegregation efforts in Virginia and other states that had a dual segregated college system.

"We'll look at it real hard," said James C. Turner, a Washington attorney for the fund. "It seems premature at this point."

Turner said the latest federal review in July found serious fault with desegregation efforts at Virginia State University in Petersburg, one of two traditionally black state-supported schools in Virginia.

The other is Norfolk State University in Norfolk.

"The traditional black institutions have not been brought up to the standards of the traditionally white institutions," Turner said. "It's hard for me to see how that's living up to commitments."

The state's proposal also drew a cautious response from Elwood B. Boone of Petersburg, a member of a biracial committee appointed by the governor to oversee programs to improve the educational opportunity of blacks.

Boone, a professor for 40 years at Virginia State, said he was concerned that the administration after Robb, who cannot succeed himself, may not be as progressive on racial matters.

"I would be reluctant . . . we don't know what a new governor and General Assembly will do. The Robb administration goes out in January. I've never heard what [the candidates to succeed Robb] are going to do."

In the past two school years, Virginia officials said, they met their goal of enrolling about 4,000 new black students at the state's 13 traditionally white public four-year institutions, and exceeded their goal of enrolling about 500 white students at the two traditionally black public institutions. Blacks make up about 19 percent of Virginia's population.

Black enrollment at the University of Virginia in Charlottesville has risen from 2.6 percent in 1978 to 8.3 percent in 1984, the latest figures available.

At George Mason University in Northern Virginia, which has experienced rapid growth, blacks account for 3.87 percent of the approximately 14,000 students, compared to 2.4 percent in 1978 when it had about 7,400 students.

Late today, Robb's office said the civil rights office had taken the request under advisement, but did not indicate how it may respond.

"The commonwealth is pleased to report that all good faith commitments to achieve numerical goals . . . have been implemented," Virginia Secretary of Education Donald J. Finley said in his letter to federal officials.

The desegregation agreement has been the focus of several politically sensitive revisions since its inception, with attorneys for the NAACP fund charging that Virginia repeatedly had failed to make good its desegregation commitment.

The state agreed to a new five-year plan in 1978 under then-Gov. John N. Dalton (R) but fell far short of its goals.

In a controversial revision of the plan in 1983, the Robb administration revised downward the goals for integrating students and faculty in the school system.

That plan, which expires next year, generally has won high marks from federal officials.

The exception has been Virginia State where the school administration has been embroiled in controversy over how it has spent millions of dollars in funds that were intended to enhance the academic programs.

In effect, the Robb administration argued today that the state has done virtually everything it can to provide more resources to the school but that under Virginia's autonomous system, Virginia State must make the final decisions on how to improve its services.

The governor appoints the governing board of visitors for each of the state's 15 major four-year public institutions and 25 of its two-year state-supported schools.

"It's kind of a punt, isn't it?" countered Turner, the NAACP lawyer, who argued that the state still has the responsibility to see that the colleges implement the state-imposed requirements.