President Reagan has agreed to export Alaskan crude oil starting next year, and Japan is expected to be a customer, administration officials said yesterday after Reagan's meeting with Japanese Prime Minister Yasuhiro Nakasone in New York.

The amount of crude is a relatively small 6,000 barrels a day and will come from the Cook Inlet area of Alaska.

Reagan needs only a Commerce Department license to export oil from there but must win congressional approval to export from Alaska's North Slope.

A White House spokesman said, "There is no current consideration of exporting North Slope oil." Nonetheless, Reagan's action will make the United States an oil exporter for the first time and earn it an estimated $61 million a year at today's oil prices.

News of the president's decision came from Alaska Gov. William Sheffield (D) after he met with Nakasone in Anchorage, who stopped there briefly en route to Japan from the U.N. meetings in New York.

Administration officials here stressed that Japan is not the only country that could purchase Cook Inlet oil and said the action by Reagan should not be read as a significant move in the context of U.S.-Japanese trade relations. However, an administration official said, "If this leads to some betterment of the trade situation, that's fine with us."

Alaskans, including Republican Sens. Frank H. Murkowski and Ted Stevens, have been pushing to free Alaskan oil -- including that from the North Slope -- for export. Sheffield told United Press International that if Congress were to approve the sale of North Slope oil to Japan, it could bring up to $2 billion a year to the United States and make a dent in the trade deficit with the Japanese, estimated at $50 billion this year.

The economics of transportation are such that the lower 48 states can get oil cheaper from South America and Mexico than from Alaska, while the Japanese are a natural market for Alaskan crude. "We will have to replace the export oil," the spokesman said.

Opposition to exporting Alaskan oil has come from maritime interests and the administration is expecting to hear from them about this decision, which does not require that oil be shipped on American tankers.

Sheffield also said Japan will lower its timber tariff to make American forest products more marketable.

Although that tariff will not come down until April 1987, Sheffield said Nakasone would work to lower it sooner. Administration officials said there was no relationship between the timber and oil actions.

A senior administration official who briefed reporters on Reagan's meeting with Nakasone Friday said the "bulk" of their discussion was on the trade deficit, the relationship of the yen to the dollar, protectionism and opening Japanese markets to U.S. exports.

Reagan "indicated his appreciation for everything Nakasone has done with regard to opening markets, but stresssed that it is important that we continue these efforts. He said, for our part, that we will continue to do all we can to avoid going down the road of protectionism," the administration official told reporters.