A controversial proposal to authorize the export of crude oil from the North Slope of Alaska has been rejected by the Reagan administration's Cabinet Council on Natural Resources and Environment.

Both houses of Congress would have to approve any exports. In the face of heavy bipartisan opposition, the council, headed by Interior Secretary James G. Watt, decided not to recommend that the president seek the waivers, according to informed sources.

Reports of the council's decision have been circulating for several days, but no official announcement has been made, and government officials say they have been instructed not to discuss it. Danny J. Boggs, chairman of the interagency group that presented the export proposal to the Cabinet Council, declined to discuss the reports and said yesterday it was possible that no announcement would be made.

However, Rep. Stewart McKinney (R-Conn.), a strong opponent of exporting the oil, said he had confirmed that the Cabinet Council had taken up the proposal and had rejected it. He said he was "heartened that Chairman Watt and other members of the council have agreed with Congress that the export ban is still essential" to U.S. economic and military security.

The issue before the cabinet group was whether the administration should seek congressional approval to authorize the export to Japan of approximately 500,000 barrels a day of Alaskan crude that now is shipped through the Panama Canal to refineries on the Gulf of Mexico.

The maritime industry lobbied furiously against the proposal because it would have opened up the oil transport traffic to lower-cost foreign shipping. A paper submitted to the council by the Boggs group said 2,840 workers in the shipping industry would have lost their jobs and 49 U.S.- flag tankers would have been "laid up or scrapped."

As presented to the Cabinet Council, the group's paper said net federal tax revenues probably would increase by $224 million to $315 million annually because of taxes on increased oil company profits.