The Carter administration's first attempt to use public criticism to hold down price increases was dealt a serious blow yesterday when Bethlehem Steel Corp., the second-biggest producer, said it would follow the lead of U.S. Steel Corp. and boost prices on two of its product lines.

Shortly after U.S. Steel announced price increases on tin mill products and structural shapes Thursday, Charles L. Schultze, chairman of the President's Council of Economic Advisers, called the boosts excessive and "inconsistent" with President Carter's attempts to hold down inflation.

The unusually swift and sharp criticism was aimed at inducing other steel producers to hold the price line and not follow the industry glant's lead. Bethlehem's announcement yesterday virtually insures that other major steel producers will follow suit and raise prices on these two products on Sept. 4.

Structural shapes, which are used in heavy construction like manufacture of plants and bridges, are more important to Bethlehem's overall output than to U.S. Steel's.

Schultze, in criticizing U.S. Steel's move, said it was the fifth time since December that steel companies have raised prices. If the increase was followed by the rest of the industry, steel prices would be 12.5 per cent higher than a year ago, he said, while overall industrial prices have risen 7 per cent in the same period.

Both U.S. Steel and Bethlehem will raise structural prices 6 per cent and tin mill prices 7 per cent. Tin mill products are used to make beberage containers and tin cans.

Schultze insisted that the administration was not interested in asking Congress for power to control or delay prices, despite the President's disappointment at U.S. Steel's move. He said the administration continues to favor a voluntary approach to inflation control, although he said the government needs help from the private sector.

U.S. Street, in announcing its increases, cited increasing costs. Government economists do not dispute the cost increases, but note that demand for structural product is low and that imports of both structural and tin mill products have been increasing.

The comptroller's regional office in Chicago under administrator Billy C. Wood, who moved there recently from Atlanta, was told to start working on the case. In Washington, a spokesman for Comptroller John G. Heimam said:

"Whenever information comes to the attention of the office of the Comptroller of the Currency that raises questions under the laws applicable to national banks, the office of the comptroller immediately takes the necessary steps to ascertain the facts and then follows up with whatever action is appropriate."

Lance said in a statement issued by the Office of Management and Budget yesterday afternoon that he is "prepared to answer fully" any questions the Senate committee has for him Monday. In a companion statement OMB officials declared again on Lance's behalf that "there is absolutely no relationship" between the Georgia bank's correspondent banking arrangement with First National of Chicago and Lance's loan.

Administration economists calculate that steel companies are using only 35 per cent of their capacity to produce structural steel, and hope that demand is so weak that companies will not be able to make the price increases stick.

The demand for tin mill products is better - the industry is working at about 83 per cent of capacity - but this will be the second rise in tin mill prices this year.

Tin mill product imports are up 85 per cent during the first five months of the year and structural imports have risen 49 per cent, according to government figures. The price increases will make it easier for foreign steel producers to make further inroads into the U.S. market, Schultze said.

This week's confrontation between steel companies and the White House is the latest chapter in a saga that goes back at least to 1952 when an angry President Truman tried, unsuccesfully, to nationalize the steel industry.

President Kennedy's most celebrated industrial confrontation was with U.S. Steel in 1962. Bethlehem Steel's decision then to hold the line forced the industry leader to rescind a price boost.

Shortly after he took office, President Ford and U.S. Steel faced off over a price increase. And last December, as he was preparing to leave office, his administration against was publicly jawboning a U.S. Steel price increase that, as usual, became standard for the industry.