The steel industry said yesterday it is becoming increasingly skeptical that the government's program to hold down steel imports will work and promised to push for new legislation that would impose quicker and heavier penalties on countries found to sell their products below fair value in the United States.

George Stinson, chairman of National Steel Corp., told reporters that a new study showed that the American steel industry lost $4.1 billion in 1976 and 1977 because of "massive dumping" of steel by foreign producers.

He said that dumping in those two years cost about 30,000 American jobs.

Stinson said in a later interview that he has not yet given up on the so-called trigger price mechanism developed by the Carter administration to reduce illegally priced steel imports, but that if they do not begin to have a substantial impact by Aug. 1 he would have to conclude that they are not working.

The Carter plan sets minimum prices for steel imports based on the cost of production and transportation of the world's lowest cost producer Japan.

Stinson conceded that nearly all steel producers are experiencing a big upsurge in orders during the second quarter, some of it due to increased demand for steel and some of it because the trigger prices keep out undervalued steel.

But he said the trigger prices are too low and that they should be increased by between $25 and $40 a ton.

Mark Anthony, president of the California-based Kraiser Steel Corp., said the trigger prices are doing little to keep Japanese steel out of the West Coast markets because the trigger prices are the lowest on the West Coast.

Because the trigger prices include transportation charges, West Coast prices are cheaper than those in the Midwest or East Coast because Japan is closer to Los Angeles than to Chicago or Pittsburgh.

The Carter administration designed its minimum price system under heavy pressure from steel companies, steel workers and Congress - all of whom were convinced that unfair European and Japanese steel marketing was costing American workers job.

Major steel companies have been waging a campaign against foreign steel for years, but only recently have they been joined by their labor unions, becoming a potent force in Congress. Protectionist sentiment has been growing in Congress not just for steel but among industries as widely dispersed as color televisions, shoes and fasterners such as nuts and bolts.

President Carter's chief trade negotiator Robert Strauss has negotiated a number of voluntary restraint agreements with countries supplying shoes and televisions, but by far the most comprehensive program to restrict imports was the trigger price mechanism devised by a task force headed by Treasury Undersecretary Anthony Solomon.

The mechanism relies on the same anti-dumping laws that steel industry officials said yesterday they want to toughen. If steel is imported into this country at a price below the trigger price, an immediate investigation is launched to determine whether the item is being sold below the cost of production, which is illegal under U.S. law.

If the item is found to be in violation of trade laws, the Treasury then slaps on a special tariff.

The trigger price system is designed to speed up an anti-dumping investigation, reaching a tentative decision in three to six months, rather than the year or more it takes under normal anti-dumping procedures.

But the existence of trigger prices, which were just revised upwards, is supposed to eliminate unfair trade before it occurs, on the theory that foreign suppliers will not test the system by selling below the trigger price.