PITTSBURGH (AP) _ Steel imports hovered near record highs during the first quarter as American producers continued waiting for President Reagan's trade restraints to take effect, the American Iron and Steel Institute said Tuesday.

The United States imported 2.03 million tons of steel products during March, compared with 2.05 million tons in February and 2.22 million tons during March 1984, the Washington-based trade group said, quoting Commerce Department figures.

''During the first quarter of 1985, we witnessed the dismal spectacle of over 6.7 million tons of steel imported into the United States, accounting for almost 28 percent of the market,'' said Donald Trautlein, chairman of the industry group.

''In the same quarter, American steel companies experienced more financial losses, more shutdowns, more layoffs, and a filing under Chapter 11 of the bankruptcy law,'' he said. ''And during the same period, almost 30 percent of America's already reduced steelmaking capacity lay unused because of lack of orders.''

Trautlein said the steel industry had not yet begun to feel the relief promised by Reagan when he announced last September that quotas would be negotiated with leading foreign sources in a bid to hold imports to about 20 percent of the U.S. market.

''Most countries are continuing to ship steel into the United States as if the president's steel program did not exist,'' he said.

Fred Lamesch, president of the American Institute for Imported Steel, said steel imported during March was ordered last fall in ''heavy buying to beat the clock'' on the Reagan administration's import restraints.

Because each country's U.S.-bound shipments will be counted against their annual quotas, excesses now could lead to sharp reductions later this year.

Shipments from Japan, the largest single source of the nation's steel imports, stood at 1.7 million tons through March, up 79,000 tons from the 1984 period. Japan's shipments increased from 507,000 tons in February to 566,000 tons in March.

Shipments from the European Economic Community fell from 586,000 tons in February to 505,000 tons in March, although the year-to-date total of 1.8 million was up from 1.3 million tons in the 1984 first quarter.