The pressure is now on the U.S. Trade Representative's office. President Reagan's decision two weeks ago to reduce steel imports through voluntary restraint agreements puts the heat on Trade Representative William E. Brock's aides to negotiate deals with a number of exporting nations during the next six weeks.

Brock has said a few countries, maybe only five or six, would be asked to curb their exports. He named Spain and Brazil as countries that would have to sign agreements to avoid unfair trade practice findings that could, in effect, bar them from the U.S. market. He also cited Japan and Korea as having led the Reagan administration to come up with a new definition of unfair trade practices -- "diversion," a reference to foreign quotas that leave the United States as the only market open to imports.

Brock cited Japan's low level of imports, 4.9 percent, and suggested that the United States would be better off if Tokyo took more steel from Korea.

Imports have averaged 25.8 percent of the U.S. market this year. The president said his program should reduce that share to 18.5 percent.

Deputy U.S. Trade Representative Robert E. Lighthizer is expected to begin informal consultations soon with most of the nations that sell large amounts of steel here.

It is unlikely Lighthizer will try to negotiate voluntary agreements with most of those nations. But a U.S. Trade Representative source said a major goal will be to persuade them to abandon unfair trading practices -- including quotas that limit Japanese steel in the European Community and non-tariff barriers that keep Japan's imports low.

Backing up Lighthizer will be steel specialists in the office of Assistant U.S. Trade Representative Charles Bloom, while Brock's other deputy U.S. trade representative, Michael Smith, will be watching the overall strategy.

Canada and the European Community, major exporters of steel, are likely to retain their share of the U.S. market, although the United States seeks sharp cuts in the amount of pipes and tubes that the EC sells here. Imports of steel pipes and tubes, which are not covered by the United States' two-year-old agreement with the European Community, represented 55 percent of the U.S. market in August.

The steel industry, meanwhile, wants all exporting nations to cut back their sales in the United States. Donald H. Trautlein, chairman of Bethlehem Steel Corp. and head of the American Iron and Steel Institute, said lowering imports to 18.5 percent will require everyone to shave their exports.

Chaparral Steel Co. of Midlothian, Tex., the nation's 10th largest manufacturer, has gone further. Last week, it formally asked Brock's office to include Poland and Norway in negotiations to control sharp increases in imports.

The Texas company said that imports of structural steel coming from those countries "at abnormally low prices" have surged into the American market this year. Norway's imports of wide flange beams, for instance, jumped from 108 tons last year to 23,217 tons in the first seven months of 1984.

The same was true for Poland, according to the company's petition. The 15,921 tons of structural channels, a kind of structural steel, that were imported during the first half of 1984 were double last year's sales here.

So Brock and Lighthizer may have to add Poland and Norway to the list of countries they need to negotiate voluntary agreements with in order to make Reagan's steel program work.

Brock, the former chairman of the Republican National Committee, will be out of town a good part of this month on the political hustings.