The Justice Department has launched an extensive investigation to determine whether the nation's top steel producers illegally have fixed the prices of hot-rolled sheet steel, a major industry product.

Department officials confirmed the probe yesterday after several major steel makers disclosed that they had received requests for information on their price increases over the last three years from the Antitrust Division.

The investment was begun after a round of price increases announced by the industry in May, according to a division official. "What we're looking for is any evidence of collusion among the steel companies prior to any of the price increases over the last three years," he explained.

"One of the things we are interested in, although it is not necessarily the primary focus, is whether there was any signalling among the steel companies on prices either through public statements or private communicators prior to those price increases."

Within the month prior to the last round of price increases, several executives of steel companies made speeches and other public statements about the need for price increases and the fact that they were examining possible price increases or would announce increases in the near future.

Noting that speeches and statements to the press are covered by the First Amendment, a division official said its only interest in the public statements is to determine whether they could have been part of a conspiracy to fix prices.

The division said civil investigate demands - the equivalent to the subpoenas used in criminal, investigations - were sent out last Thursday to 10 steel companies. The list apparently includes United States Steel Coro., Bethlehem Steel Corp., National Steel Corp., Jones & Laughlin Steel Corp., Youngstown Sheet and Tube Co., Armco Steel Corp., Republic Steel Corp., Inland Steel Co., and Wheeling-Pittsburgh Steel Corp.

For now, the division is seeking information only on hot-rolled sheet steel, a rough-finish product that is used for a variety of industrial applications, in the interiors of buildings and some large household appliances such as refrigerators and stoves, and for car parts, though not body exteriors.

Hot rolled sheet also is processed into cold-rolled sheet steel, a smooth-finish steel used in major consumer appliances and auto bodies. Hot and cold-rolled sheet steel account for about 40 per cent of total industry shipments.

Since wage-price controls were lifted in April 1974, the price of hot-rolled sheet has risen 61 per cent.

Department officials, including Attorney General Griffin B. Bell, have been taking for several months about their concerns over "lockstep" pricing by members of concentrated industries, and the division has begun a systematic review of those industries and their pricing practices.

Although the steel-price investigation is not part of that eview, the question of whether companies may be "signalling" to one another through public statements is common to both.

In a speech last month, John H. Shenefield, acting assistant attorney general for antitrust, explained the department's concern. "If prices of the industry's product seem to move in lockstep, are those prices truly the result of independent judgments on the receipts necessary to provide an adequate return on investment - or do they reflect a consenus?" he asked.