Administration officials have privately warned the U.S. steel industry not to put into effect a major price increase, in the wake of yesterday's government-announced program to discourage "dumping" of steel by foreign producers.

A big price increase for domestic steel, government officials said, could "dissipate" the benefits the domestic industry is likely to achieve as imports tapers off.

The new program would set up a system of "trigger" or reference prices, based on the full costs of production by the most efficient foreign producer currently Japan.

In effect, a monitoring and accelerated antidumping procedure would keep out imports below such a reference price, well above the level at which much foreign steel has been sold here.

Under Secretary of Treasury Anthony Solomon, author of the new antidumping program, said yesterday that American producers might recapture as much as half of the import volume they had lost because of deep-discounting.

Imports have been running at about 20 per cent of U.S. steel consumption, compared to an average of 13 per cent from 1973 through 1976. Solomon said that if the antidumping program is a success, the foreign share might be reduced to 12 to 14 per cent.

But in a telephone interview, Barry Bosworth, director of the government's price-monitoring agency, the Council on Wage and Price Stability, said that "the extent to which the industry regains a share [of imports] depends heavily on its own pricing practices."

In effect, government officials hope that the industry will respond by boosting production and employment, rather than trying to widen price differentials with the new and higher import levels.

For the next four or five months," Bosworth said "I think you will see a dramatic reduction in imports. After that it's up to the domestic industry."

Some modest domestic price increases are considered inevitable, and there will be future cost pressures arising from coal and iron ore costs," officials say. But what the Washington economic doctors are counting on is the industry keeping as close as it can to the "trigger" price.

Bosworth agreed with Solomon's analysis that the antidumping proposal would prove to be the last inflationary of any of the options available to deal with the short-term crisis of the steel industry.

The Carter administration took pains to deal with the political pressures to salvage domestic steel jobs without giving way to openly protectionist solutions such as physical quotas on imports.

It also rejected the desire of European steel producers for a multilateral agreement that would have carved up the market among existing producers, and frozen out smaller, developing nations.

As it stands, the system excludes no seller who prices his steel at cost or above, and thus assures a range of flexibility in which Japanese, European, and other sellers can maintain competitiveness with U.S. producers.

In effect, in dealing with the steel industry's short-term problems, the administration asserted a responsibility to assure that competition remains within reasonable bounds, eliminating only what it defines as unfair competition.

For the longer-term, the program holds less promise. As one analyst pointed out yesterday, plant modernization the government hopes for will essentially remain in conflict with the goal of higher employment, until there is a major expansion of economic activity.