American steel makers conditionally withdrew a major trade complaint against Japanese exporters yesterday and gave U.S. Trade Representative William E. Brock three weeks to negotiate a settlement of the dispute.

Brock announced that he will go to Japan next week to seek "an acceptable solution" to the issue. The steel makers said that, if no settlement is reached by Feb. 23, they will refile their petition for government relief against allegedly illegal Japanese imports.

Yesterday's actions defused temporarily one of the numerous irritants afflicting trade relations between the United States and Japan. It resolved nothing, but it gave Brock time to maneuver.

In the wake of last month's visit to Washington by Japanese Prime Minister Yashuhiro Nakasone, the Reagan administration is exploring a variety of formulas for resolving the nagging trade disputes clouding U.S.-Japanese relations. In a letter to David M. Roderick, chairman of the American Iron and Steel Institute, Brock expressed "appreciation for the cooperative spirit you have shown" in pulling back the petition.

Yesterday was the deadline for Brock's office to decide whether to accept and prosecute the steel makers' complaint, filed Dec. 16, that the Japanese had entered into an elaborate conspiracy with their counterparts in Western Europe to divide world markets and divert their excess production to the United States.

The American manufacturers, whose mills are producing only about 40 percent of capacity, asked for quotas and a surcharge on imports from Japan. Similar cases filed earlier against steel makers in the European Common Market countries provoked intensive negotiations between the United States and the Europeans, leading to export limits in Europe and the withdrawal of 93 separate complaints by the American mills.