The Reagan administration and the leadership of the AFL-CIO, who have spent the last two days here trying to find a point of agreement on how to right the nation's errant economy, today agreed to disagree on a major point in the discussion: A quota system for curbing Japanese competition in the auto industry.

After listening to a personal appeal from Bill Brock, President Reagan's special trade representative, to accept negotiations rather than quotas, the federation's 35-member executive council adopted a policy calling for legislation that would place import quotas on Japanese cars.

The two sides have been polite, even gracious in their encounters with one another here at the annual midwinter meeting of the federation's executive council, and Monday, in a friendly session with Senate Majority Leader Howard H. Baker Jr. (R-Tenn.), the two sides acknowledged that they probably could do more to help the country by working together than by working apart.

But the difficulty in achieving such a rapprochement between organized labor and its traditional opponents in the moderate-conservative wing of the Republican Party was highlighted by the quota issue.

The federation stuck to its position that "immediate import relief" is needed to help domestic industries such as auto, steel and textile manufacturers, which the AFL-CIO believes have been harmed by foreign competition. "Immediate import relief" in the federation's parlance means some form of federally imposed restrictions on the importing of some products so that domestic industries can recover from their economic slump.

Brock, talking to reporters before a breakfast meeting with the council, said, "I do think that there are times when a major domestic industry is in serious trouble, that you have the right to seek from your trading partners around the world some understanding of that problem, and some restraint on their part."

But he added: "I think it would be very difficult to support legislated quotas [on imported products] when, sometimes, you can get a much more rational agreement through negotiations."

Council members said in interviews after the meeting that Brock stuck to his position, and that the federation's leaders stuck to theirs.