If major steel companies decide to file anti-dumping complaints against foreign producers, the government is likely to junk its two-year trigger price program designed to set a minimum price for inported steel, sources said.

U.S. Steel Corp., the nation's largest, already has complaints ready to be filed against European countries and is working on a similar complaint against Japan. The next largest steel companies -- Bethlehem and National -- are also preparing their own cases against foreign steel makers.

In a related development, the General Accounting Office, the congressional watchdog agency, has concluded that the Treasury Department was lax in its enforcement of the trigger price program. Between October 1978 and March 1979, the GAO found 355,700 tons of steel that were imported below trigger prices, according to Dow Jones News Service.

The criticism of the Treasury comes in and as yet unreleased draft study.

Since the GAO investigation, however, enforcement of the nation's trade laws has shifted from the Treasury to the Commerce Department, a development that most industries seeking protection from foreign competition have lauded.

Throughout all administrations, Treasury officials have been generally "free trade oriented" and the agency has tended to look askance at cries from industries that foreign competition was unfair.

In late 1977, under heavy pressure from both the steel industry and the United Steel Workers, the administration fashioned a compromise strategy to insulate U.S. steel producers from unfair competition.

Part of the plan involved the institution of so-called trigger prices, which were based on the cost of making steel in Japan and shipping it to the United States. Japan is generally considered the world's most efficient producer of steel. But the U.S. industry long claimed that it could compete with Japanese steel producers in the United States if Japan was forced to price its steel at the cost of production and shipping.

European producers are less efficient than either the United States or Japanese steel makers.

Treasury officials said that they could not process both trade complaints from steel producers and enforce the trigger price program. In early 1978, after trigger prices went into effect, steel producers withdrew most of the anti-dumping complaints they had filed with the Treasury.

However, they said that if the trigger price program was not effective they would re-file anti-dumping complaints.

Although the trigger price program appears to have reduced steel imports somewhat, the reduction was not big enough to the liking of either the producers or the union.

The Commerce Department is scheduled to recalculate the trigger prices next week, and one highly placed steel maker said the industry, including U.S. Steel, would wait until the new prices are announced before making a final decision on whether to file the new dumping complaints, which allege that major European producers are selling steel in the United States at less than the cost of production and that this dumping is hurting American industry and workers.

Because the dollar has been appreciating against the yen in recent months, it is unlikely that the Commerce Department will set trigger prices that are much higher, if at all, then those in effect for the first quarter of 1980.

In a related steel industry development, U.S. Steel Corp., seeking foreign expertise to help it streamline its ailing steel operations, signed a three-year contract for technical aid from Nippon Steel Corp. of Japan, the non-Communist world's largest steel maker.

The contract calls for Nippon to supply technical advice over the next three years on ways U.S. Steel can increase the productivity of its blast furnaces.