A top Treasury official said Wednesday that the government expects to file its first formal charges against foreign steel makers under the special, 4-month-old system of minimum prices for steel imports designed to protect domestic makers.

Anthony M. Solomon, Undersecretary of the Treasury for Monetary Affairs and the architect of the so-called trigger price program, told reporters he thought the agency would being to file several formal anti-dumping investigations within a few weeks.

In an earlier address to the world's steelmakers gathered here, Solomon said that the trigger price program "has functioned satisfactorily so far" in preventing foreign steelmakers from selling their product below cost in the United States.

But Solomon said the U.S. government was disturbed by a big jump in steel imports during July and August, after they decided in May and June (the first two months of full operation of the trigger price program).

Solomon said that while experts do not think the high level of imports will persit "we will monitor future conditions carefully and respond appropriately."

But under questioning, Solomon would not say what the government might do if steel imports remain near their current levels. It would "depend on the circumstances," he said. "It could be anything."

He did, however, rule out either scrapping the trigger price program or setting up a special two-tier system of minimum prices, with one tier aimed at Japan and the other at the rest of the world, especially European steelmakers.

While Japanese steel exports to the United States, have not risen much, European community steel-makers, with the exception of the British, have sharply increased their sales to the United States. Imports from developing countries have also accelerated. Sources said yesterday, that Solomon had privately met with some European steelmakers, presumably to convince them to moderate their steel exports to the United States.

The world steelmakers are gathered here for the annual meeting of the International Iron and Steel Institute.

The trigger price system in effect, sets minimum prices for foreign steel imported into the United States. The prices are based on the cost of production in Japan plus shipping to the United States. The Japanese are thought to be the world's most efficient steel producer.

If steel is imported below trigger prices, the Treasury begins an informal investigation to see if the sale is in violation of U.S. anti-dumping laws, which among other things prohibit sales below cost. However if a producer can demonstrate that the price is not in violation of U.S. laws, the Treasury will not proceed with a formal investigation.

Solomon said yesterday that the Treasury has undertaken more than 200 of these preliminary investigations and concluded that none of the sales below trigger price was in violation of the law.

But he said there "is a strong likelihood" that the government will file formal anti-dumping charges against several foreign steel producers within a couple of weeks. He did not say which countries would be involved.

Most domestic and foreign steelmakers, gathered here for the annual convention of the International Iron and Steel Institute, said they favored the trigger price mechanisim and that the program must be tested over several more months.

In another development, H. J. Holschuh, deputy secretary general of the IISI, said the outlook for the world's steel industry remains bleak. "The general and sustained upturn (in steel demand) for which we have been waiting now for a number of years is still not within sight, at least not for the industrial countries of Western Europe or Japan."

The U.S. industry has fared better than the world industry recently, although most domestic steelmakers are now scaling down their predictions of 1978 and 1979 domestic shipments.