The Reagan administration yesterday slapped tough trade restrictions on all imports of specialty steel products "to help the American worker" and protect the domestic industry from "the pervasive nature of unfair trading practices."

President Reagan said the aim of his four-year combination of quotas and tariffs is to force other nations to switch to a competitive trading system in specialty steel. He held out the possibility that the United States might agree to increase quotas for countries that end subsidies on speciality steel exports and open their markets wider to U.S. goods.

But the effect of the presidential order--which hits about 20 nations, including Japan, Canada and some of America's closest allies in Europe--was to increase concern that the United States is taking a protectionist turn despite the free-trade pledges of the Reagan administration.

U.S. Trade Representative William E. Brock emphasized the administration's commitment to free trade, but said it must enforce U.S. laws against unfair trade practices to hold down protectionist pressures.

"I am hopeful we have used a sufficiently strong two-by-four to indicate that we just can't continue to tolerate a world system that is totally trade-distortive, where governments intervene at will without any consideration of international rule," Brock said.

Brock said the Reagan decision on specialty steel is consistent with the commitment to free trade made at the Williamsburg economic summit in May.

Representatives of some other nations, however, disagreed. "It's a bad day for Williamsburg," commented a Western diplomat who attended the Brock briefing.

The decision comes as many of America's allies are questioning the administration's trade goals in light of a series of moves aimed at protecting U.S. industries from foreign competition--all taken under the rubric of combating unfair trading practices of other nations. These include asking Japan to continue limiting auto exports to the United States, setting high quotas on the imported heavy motorcycles and selling subsidized wheat flour to Egypt to capture a market from the French.

Industry and labor representatives, however, found the Reagan action "deeply disappointing" and "inadequate." A joint statement by Albert J. Lena, chairman of the Specialty Steel Industry of the United States, and Lloyd McBride, president of the United Steelworkers of America, said tariff levels on the flat-rolled product, which accounts for 75 percent of industry sales, are too small to stop other countries from overcoming them with increased subsidies. But both men approved of the quotas on stainless steel bar, rod and alloy tool steel.

Specialty steel is a low-volume, high-value product considered vital to national defense, telecommunications, aerospace and oil refining. It accounts for just 2 percent in tonnage but 10 percent of the dollar value of U.S. steel production. The White House said the United States imported $373 million worth of specialty steel last year, about 20 percent of total sales in this country.

President Reagan, faced with a series of options prepared by his trade advisers, made the decision shortly before noon yesterday at his Santa Barbara, Calif., ranch before leaving for a speaking engagement.

The U.S. International Trade Commission had recommended in May that Reagan grant relief to the specialty steel industry to overcome unfair trading practices of other countries. The ITC, which started its investigation at Reagan's instigation last November, recommended three years of relief, while the industry wanted five-year quotas.

Under the complex Reagan formula, the tariffs and quotas are imposed for four years, with the tariffs decreasing each year while the amount of specialty steel allowed to be imported increases.

Tariffs rather than the more severe quotas were placed on two forms of flat-rolled products that make up 55 percent of all specialty steel imports, because that section of the industry is the most competitive, Brock said.

The tariffs, added to the 10 1/2 percent duties already in force, start at 10 percent the first year for sheet and strip and decrease in steps to 4 percent the fourth year. The added tariff on plate starts at 8 percent and goes down to 4 percent.

Quotas were imposed on other products because the administration found that the ability of U.S. producers to modernize had been hurt by competition from low-priced imports. The quotas limit bar steel imports from all countries to 27,000 tons over the next year, rising to 29,500 tons in the fourth year; rod steel quotas are set at 19,100 the first year and 20,900 the fourth; alloy tool steel, 22,400 the first year to 24,500 the fourth. Last year the United States imported 40,053 tons of bar, 21,881 tons of rod and 40,058 tons of alloy tool steel.

The quotas and tariffs apply to all countries selling specialty steel to the United States. The major suppliers listed by the White House are Japan, West Germany, Sweden, France, Spain, the United Kingdom, Brazil, Canada, South Korea and Italy.