Rhetorically, President Reagan is a pure free-trader -- even on the political hot potato of Japanese auto exports. But behind the scenes the administration keeps pounding away at the Japanese to impose tight restrictions on car shipments.

The upshot is not merely confusion in the public dialogue and disarray within the administration. The greater danger is the loss of the truly good deal that could be cut with Tokyo by a more straightforward approach.

Publicly, the president's position finds most recent expression in a statement on the auto industry read for him by Vice President George Bush on Monday, April 6. The statement cited the terrible woes of the industry -- corporate losses at over $4 billon last year; production at a 19-year low; nearly half a million workers laid off.

Nevertheless, the president stuck bravely to his free enterprise guns. He gave the industry relief mainly in the form of an abatement of regulations. He conferred no tax benefits. Of Japanese imports, he said: "We will minitor the effect of international trade on our domestic auto industry. We are committed to free trade and believe free trade benefits all nations concerned."

Previous reports have Reagan moving stedily against protectionism. On March 19, at a session of the Cabinet, he was said to be siding with his chief domestic economic advisers -- Treasury Secretary Donald Regan; Budget Director David Stockman; and the Chairman of the Council of Economic Advisers, Murray Weidenbaum -- against pressure from Transportation Secretary Drew Lewis, for a limit on Japanese exports.

On March 24 when the Japanese Foreign Minister Masayoshi Ito visited the White House, the president said merely that there were being readied in the Congress measures that would cut Japanese imports from roughly 2 million annually last year to 1.6 million annually for the next three years. The implication was that Reagan opposed those limits . A day later, at a meeting with his prestigious Economic Policy Advisory Board, Reagan seemed apologetic for even having mentioned the possible legislative action.

Deep inside, however, the administration is playing much harder ball with the Japanese. On March 20, the day after the Cabinet meeting, Secretary of State Alexander Haig spoke personally to the Japanese ambassador in Washington, Yoshio Okawara, on the subject of cars. He also instructed Ambassador Mike Mansfield to take up the subject at the Japanese Foreign Office. The Japanese came away from those conversations convinced that the administration was asking them to cut back exports voluntarily to 1.5 million cars annually. But after seeing the president, and getting a whiff of the free-trade atmosphere in Washington, Foreign Minister Ito let it be known he was not getting a clear signal from the administration.

On April 2, after a Cabinet meeting, there was a session on cars among Secretary Haig, Secretary Lewis, trade representative Bill Brock and the two top White House aides -- Edwin Meese and James Baker. The White House said there was no accord then on a quota for Japanese autos. Other sources claim that, with the domestic economic adivisers excluded, there was an understanding that Washington should press Tokyo for the 1.5 million limit.

In fact, there is little chance of getting the Japanese to go down to 1.5 million cars by voluntary agreement. The Japanese auto industry sees the possibility of some big years ahead in the American market, and will not easily yield its competitive edge in small cars. Rather than take the heat from their own auto manufacturers, Japanese officials prefer to lose signals from Washington in the static about free trade.

Even if obtainable, moreover, the limit would not do much to help the American industry. Ford does not have, and will not soon have, the small, fuel-efficient cars that are in demand. Chrysler is too far gone anyway. GM is going to make it no matter what happens. The one big thing that could help the industry -- a restraint on wage and price increases -- has already been ruled out, on ideological grounds, by the administration.

But there is a double deal with Japan that could help the American economy as a whole. It consists of more moderate limits on auto imports and Japanese undertakings to accept more American agricultural products and not to flood world markets with high technology in the years ahead. Such an agreement would benefit American consumers, and help efficient American producers. It would forestall moves by the Europeans to graduate any agreement between the United States and Japan into a generally higher level of protection. But that truly promising opportunity will be missed if the Reagan administration, by its double talk, gives the Japanese a pretext for declaring they are not clear as to what Washington really wants.