Bethlehem Steel Corp., the nation's second largest producer, broke its week-long silence yesterday and announced that it would follow the lead of U.S. Steel and other producers in adopting a 6 per cent price increase.

Bethlehem's acquiescence solidified the 6 per cent boost as the new industry-wide level. The price covers sheet steel used in auto bodies and appliances and bar, plate and rod products used by industry.

Price jockeying by the major producers began last Friday when fourth-ranked Republic Steel Corp. and the Youngstown Sheet and Tube Co. annnounced increases of 7 to 9 per cent.

As the Carter administration decried those levels as inflationary and unwarrantedly high, U.S. Steel moved Monday to set a more moderate rate acceptable to the Council on Wage and Price Stability.

U.S. Steel's 6 per cent increase was soon matched by National Steel Corp., Inland Steel, the Wheeling-Pittsburgh Steel Corp., and forced a rollback by Youngstown Tuesday and by Republic on Wednesday.

Following Republic's action to meet the 6 per cent level, Robert Crandell, acting director of the Wage and Price Council said, "We are heartened that the lower increases announced by U.S. Steel seem to be taking hold."

Kaiser Steel Corp. yesterday raised its average product line price by 2.8 per cent, although the prices on certain products will "generally follow the price changes by other major steel producers," the company said.

Industry analysts and government economists alike said the more moderate increase was a shrewd move for the makers who are fiercely pushing for adminstration-imposed restrictions on cheaper foreign steel imports. Foreign steel currently sells for about $50 a ton less than domestic products.