The Department of Education has rejected desegregation plans submitted by five states for their public college and university systems, but has given them until Aug. 15 to prepare new ones and avert legal action by the government, officials revealed yesterday.

If the states do not submit acceptable plans by then, the department is obligated under court order to initiate enforcement proceedings by Sept. 15, which could entail cutting off federal education funds or taking civil action.

In letters to the governors or top education officials of Georgia, Oklahoma, North Carolina, Florida and Arkansas, dated June 30, Harry M. Singleton, assistant secretary of education for civil rights, said desegregation plans the states had been ordered to submit by Judge John H. Pratt of the U.S. District Court of the District of Columbia contained many good features, but on the whole were unacceptable and needed to be redrafted or beefed up.

In notifying the states that their plans did not pass muster, the department was complying with an order from Pratt that it decide on them by June 30.

In a news conference in Atlanta, a combative Gov. Joe Frank Harris refused to make broad changes in the desegregation plan. He said he believes the Georgia plan is sound and requires only fine-tuning. "I think we've got the problems ironed out right now," he said.

Harris was equally adamant in refusing a federal order that the regents exam be overhauled because of charges that it discriminates against black students. "That is grounds for us to go to court . . . ," he said.

The June 30 action, though not the only turndown of a state plan by the Reagan administration, is the first in which plans for a large number of states were rejected as a block.

The dispute began in 1970 when civil rights groups represented by the firm of Rauh, Silard and Lichtman brought suit to force the government to desegregate higher education in a number of states.

Elliott Lichtman, a member of the firm, said yesterday that since 1978 a number of states had been under five-year plans to desegregate, but when it appeared they would fall short of their goals, the firm asked Judge Pratt to intervene.

"The real question is whether, at the end, if the states don't submit acceptable plans, they are tough on enforcement," Lichtman said. He added that he hoped the government wouldn't "give the house away" by approving a weak plan.

The department had no comment on the turndowns, other than to say that it was carrying out Pratt's order to approve or reject the plans by June 30.