Virginia Gov. John N. Dalton appears destined to leave office next month with a major goal of his administration -- wiping out vestiges of racial inequality in state-supported colleges and universities -- still in question.

Three years after Dalton signed a controversial pact with U.S. civil rights officials designed to erase historic racial imbalances in Virginia's system of higher education, federal officials say serious shortcomings remain in Dalton administration attempts to carry out the plan.

In a letter to Virginia education officials last month, Dewey E. Dodds, director of the U.S. Department of Education's Office of Civil Rights, criticized state efforts to increase the percentage of blacks going to college, increase black enrollment at predominantly white schools and white enrollment at predominantly black schools, meet minority faculty hiring goals and initiate new programs and enhance facilities at two traditionally black state universities.

The letter, which aimed criticism at "incomplete" reports submitted by Virginia to the U.S. Civil Rights Office, gave Virginia Secretary of Education J. Wade Gilley 45 days to respond.

Gilley said today that the Dalton administration will respond to Dodds' inquiry, but said some answers will require long-term gathering of data. That guarantees that Democratic Gov.-elect Charles S. Robb will inherit the politically sensitive issue when he takes office Jan. 16.

Among criticisms raised by Dodds:

* The disparity between college-going rates of black and white high school graduates in the state has widened, from 7.6 percent in 1978-79 to 10.1 percent in the 1980-81 academic year.

* Although Virginia achieved its 1979-80 goal of increasing first-time black enrollment at traditionally white institutions, only six of the 13 met their institutional goals. In the 1980-81 academic year only two of the 13 reached their goals.

* Only three of 10 institutions offering graduate programs reported efforts to recruit blacks at the graduate level, according to a 1980 state report.

* The failure to determine whether the state system as a whole is making progress toward hiring black faculty and administrators equal to the proportion of blacks receiving master's and doctoral degrees.

* Two institutions (Virginia Military Institute and Richard Bland College), Dodds said, have failed to establish any goals to hire black faculty.

* Lack of data on whether the state's two traditionally black universities (Norfolk State and Virginia State near Petersburg) now have resources comparable to predominantly white schools with similar missions.

* A failure in the state's 1980 report to indicate whether new programs for Norfolk State and Virginia State had been provided.

* An indication by the state that it may not expand an engineering technology program at Virginia State to a four-year term, which Dodds said is "inconsistent with . . . earlier commitments."

* Failure to detail plans for enhancement of facilities at the two mostly black universities.

A spokesman for Robb, who rode to victory last month on a wave of support from Virginia's black voters, declined to say today what path the Robb administration will follow in dealing with the plan.

"We are not in office yet," said Robb aide George Stoddart. "And we're not going to set policy until we are."

L. Douglas Wilder of Richmond, the sole black member of the state Senate, said he expects Robb "has a mandate to steer Virginia on a course not tied to the past."

"We've mounted a major effort," Gilley said, including a publicity campaign and a minority recruiting plan aimed at attracting black high school graduates, and a program of $1,000 scholarships for black students willing to attend predominantly white schools, and vice versa.

"I don't know what else we can do . . . ," he said. "It takes time."