Beleaguered U.S. steel makers have asked the United Steel Workers to take part in industrywide collective bargaining this month.

The request was made last week in a letter from the chief negotiator for the steel industry to USW President Lloyd McBride, who immediately summoned the union's 600 local presidents, who sit on the basic bargaining conference, to a meeting June 18 in Pittsburgh.

A knowledgeable source who asked not to be identified said the message from the eight-company bargaining group was unclear on whether the industry wants to renegotiate the third year of the current pact or start bargaining early for lower labor costs in the succeeding contract. The current contract expires in August, 1983.

Neither company nor union spokesmen would comment publicly. "They're taking a very low profile on the thing," the source said.

It's not certain whether McBride, scheduled to retire when his term expires in 1984, would be able to obtain support within the union for reopening the current contract. The giant Local 1010 at Chicago's Inland Steel already is on record in opposition to such a move.

The nation's steel industry is in a production slump unequalled in nearly 20 years, and approximately 100,000 of the USW's estimated 375,000 steel-making members are laid off, with the threat of new shutdowns looming as the industry runs at less than 50 percent of its capacity.

The steelworkers' average hourly wage has been estimated to be $13.68. The current three-year USW contract calls for a 23-cent wage increase and a 37-cent-per-hour cost of living bonus in August.

Company officials, pressured by the loss to imports of nearly a fourth of the domestic market in the first quarter, recently have been saying high labor costs make them unable to compete with cheaper foreign steel.

The concern has spread to the auto industry, traditionally one of steel's biggest customers.

"I am concerned about . . . the viability of the domestic steel industry to produce quality product at a competitive price," General Motors Corp. Chairman Roger Smith said here last month.

Because of the auto industry's deep slump, the United Auto Workers made major wage and benefit concessions that generated significant savings to help companies through hard times.

Smith encouraged the USW and the steel makers to likewise "get together and work things out."

U.S. Steel Corp. Chairman David Roderick earlier this year said labor costs could become "insurmountable obstacles" to the industry's recovery.