The nation's major steel makers are divided over just how the industry can best spend its money to upgrade and modernize facilities and lower the costs of production.

Thomas C. Graham, president of LTV's Jones & Laughlin Steel industry does not have the finacial resources to build plants from scratch.

The steel industry must "find some other way of remaining competitive," Graham warned his colleagues at the annual meeting of the American Iron and Steel Institute here.

Graham suggested that rather than focusing on building multibillion dollars new plants, the industry should concentrate on better management of the "production processes and captial funds that are available" in order to lower the costs of production and boost profitability.

Graham's advise runs almost directly counter to the program offered Wednesday by Edgar B. Speer, chairman of industry leader U. S. Steel Corp. and outgoing chairman of the trade group.

Speer said steel companies will not be able to take advantage of important cost-saving technologies by making piecemeal changes at their existing facilities. Instead, he urged the nation's steel companies to "move aggressively" into the construction of new steel plants.

U. S. Steel has major multi-billion dollar plant on its drawing boards for an Ohio site near Lake Erie and the Pennsylvania border. Despite Speer's insistance on the need to build such plants, the company has not yet decided to make the investment, in large part because of finances.

Graham head of the nation's seventh-largest steel company, said in effect yesterday that steel companies are kidding themselves if they think there is a prospect for the kinds of massive new steel facilities that speer advocates.

"Since our capital resources are limited we should be more aggressively pursuing those means of productively improvement that can be achieved without major capital spending," Graham said. He citied a dozen or so examples of innovations in operations that have substantially raised productively at many steel companies, including his own.

J & L's parent company, LTV, is in the middle attempt with Lykes Corp., which controls the nation's eighth biggest producer, Youngstown Sheet & Tube Lykes, which has shut down most of the its steel facilities in Youngstown, Ohio has claimed that if the merger is not approfed by the Justice Department the company could go bankrupt.

In another development, Thomas A. Murphy, chairman of Gerenal Motors Corp., told the steelmakers last night that businessmen "must redouble our cost control efforts in every area of our operations, to take every reasonable action to stem the rising tide of both costs and prices."

Murphy noted in prepared remarks that GM pledged to hold down both price increases and excutive salary increases this year to conform to President Carter's voluntary program to slow the rate of inflation.

Steel executives such as Speer have said that while they support the President's program they cannot pledge to keep their price increases smaller than last year's.

Murphy said that if the President's program to "decelerate" inflation is to program to "decelerate" inflation is to work, government and labor must also work, government and labor must also do their share. While GM has pledged to decelerate its price increases this year, "deceleration of wages is another matter," Murphy said.

He noted that labor costs at GM will "continue to increase at an annual rate in the area of 10 percent in 1978" under the terms of union contracts.