The Federal Aviation Administration has refused to kick Supreme Court justices and diplomats out of National Airport's VIP parking lot, as some members of Congress had requested. But, warns the congressman who started it all, this is not the end of the story.

Rep. Philip M. Crane (R-Ill.), who led a recent drive to ban the justices and diplomats from the parking lot so that there would be more space for members of Congress, said yesterday that the issue probably would come up again when Congress next considers FAA appropriations.

In September, Crane and 37 other members of Congress wrote a letter to the FAA, complaining that the exclusive reserved lot just steps from the main passenger terminal often fills up with diplomats and justices "at the expense of members of Congress who truly need the ready access to parking . . . ." Although congressmen still can park free in the general lots if that occurs, the public spaces are far less convenient than the VIP lot.

In a letter dated Nov. 4, FAA Administrator Donald D. Engen replied that he had discussed the parking proposal with State Department officials and with Chief Justice Warren E. Burger before determining that it was "best to continue the present practice."

Crane called the FAA reply "totally unsatisfactory." He said he wanted to know why Engen "chose to poll the State Department" and confer with Burger, yet did not poll the 535 members of Congress. If he had, said Crane, he would have found "overwhelming" support for the parking change.

"The FAA gets appropriations annually," said Crane. "They make representations before the Public Works Committee and the Appropriations Committee, not the State Department." He said he would talk to committee members about raising the issue the next time FAA officials appear before a House committee to discuss the agency budget.

Crane said he had only 38 signatures on the letter because he passed it around only on the House floor for one afternoon. But he said he could have gotten far more signatures, adding that other members have since told him they wanted to sign the letter.

Engen said the FAA believes the best solution would be the passage of a Reagan administration bill, pending in the Senate, that would transfer authority to run National and Dulles airports from the federal government to a regional airport authority. Under the plan, the authority would float bonds to raise money for improvements, freeing the federal government from such costs.

"When the airports are transferred to an independent public au-thority, parking facilities can be improved and expanded promptly," said Engen.

Crane said that although he was not opposed to the proposal to transfer the airports to a regional authority, he did not understand why the improvements must wait until that transfer takes place.

Engen "says these things can be done promptly," said Crane. "Why can't they be done promptly now?" He suggested that the FAA contract with a private company that would run the parking lots and make the improvements.

Members of Congress, justices and diplomats are allowed to park free at National Airport. Crane said they should still be allowed to park free if a private company ran the parking lots and that the improvements could be paid for from parking receipts paid by the general public.