Citing the need for European cooperation in the air traffic controllers strike, President Reagan has asked the Civil Aeronautics Board not to life the antitrust immunity of American airlines that engage in price-fixing on North Atlantic routes.

A CAB order lifting the immunity for two years is scheduled to go into effect Sept. 15. Several European members of the International Air Transport Association have objected strenuously to the CAB order as unilateral U.S. action to undercut reciprocal air agreements.

After lengthy consideration, the CAB is planning to put its order into effect in an attempt to discourage the major American carriers on the North Atlantic routes from rejoining the price-fixing structure of the IATA.

Reagan said in a letter to CAB Chairman Marvin S. Cohen that he was "not expressing any view on the merits of the important and complex issues involved in this proceeding."

But he said that because European governments have cooperated with the United States in keeping the heavily traveled North Atlantic air lanes open during the controllers' strike. "It is especially important during this period that the United States demonstrate its continued support for an international aviation system founded on comity and reciprocity and its sensitivity to foreign government concerns."

The president asked that implementation of the order be deferred "beyond Sept. 15," but he did not say for how long.

The CAB has not acted on the president's request. A spokesman for the regulatory agency said it would have to be considered by the entire board, and no action would be taken before next week.

If the CAB rejects the president's request and goes ahead to lift antitrust immunity for Pan Am, TWA, Northwest and other American carriers, it apparently would have little immediate impact on the fares paid by travelers. The American carriers currently do not participate in the price-fixing structure, and elimination of their antitrust immunity would make it unlikely that they would do so.