For the second time in four years, Virginia and the federal government have agreed on a plan for the integration of the state's colleges and universities, this time at a cost of $16 million over three years.

The state reached an agreement on a new college desegregation plan late this afternoon with the NAACP Legal Defense Fund, the original plaintiffs in a landmark college desegregation lawsuit, and the Office of Civil Rights in the U.S. Department of Education, state officials said today.

The latest chapter in a decade-long effort to bring Virginia into compliance with the 1966 Civil Rights Act was applauded today by Gov. Charles S. Robb and top legislators, who must approve funding for the plan.

Robb emphasized his commitment to the new plan, but added, "I am less pleased by the necessity of making commitment to federal criteria which appear to measure Virginia's sincerity by numerical objectives and dollars appropriated."

Last summer, the Civil Rights office, acting under pressure from a federal court case first brought by the NAACP in 1969, found Virginia's 1978 plan to be a failure because the enrollment of black students in traditionally white colleges and of whites in traditionally black colleges had fallen behind the plan's goals.

Robb and Virginia Education Secretary John Casteen reworked the plan and submitted their amendments to Washington last September.

Negotiations began in December but collapsed briefly last week.

Funding for the plan in 1983-1984 will total $6.3 million, including $4.5 million in capital projects at Virginia State University and Norfolk State University, the state's two traditionally black public colleges.

Those projects had originally been frozen along with other state construction plans as Robb looked for ways to shore up the state's projected $305 million deficit.

Among the compromises made during negotiations was the abandonment of a so-called "bounty" plan that would have rewarded white colleges that attracted black students with a $1,000 a year grant. Still in the plan are $500,000 in grants for black students transferring from two-year community colleges into four-year colleges and a beefing up of the admissions programs at Norfolk and Virginia State, which will continue their efforts to attract white students.

The plan calls for almost a doubling of the number of black students entering traditionally white four-year colleges from 1,467 in 1982 to 2,730 in 1985. For George Mason University in Fairfax County, that will mean an increase in black freshmen from 57 this year to 300 in 1985. The number of black students at the state's 23 two-year colleges is scheduled to increase from 1,742 to 2,327. At Northern Virginia Community College, the numbers are scheduled to go from 72 to 96.

Other programs include a plan for the recruitment of black students into graduate programs and a study of reasons why Virginia has been unable to recruit or retain an appropriate number of black faculty members.

Of the $6.3 million required for next year, $1.8 had already been appropriated in Robb's proposed budget amendments, now under review by the budget committees. Money for the capital projects--$2.5 for Virginia State and $2 million for Norfolk--will have to be found during the session, Casteen said. The remaining $9.7 million portion of the plan will be funded in the state budgets during the next two years.