Bethlehem Steel Co. yesterday announced a 3 percent price increase effective July 30 and pledged to forgo further price rises this year "barring unforeseen circumstances and assuming that inflationary pressures are brought under control."

White House officials, who had feared a much steeper rise in steel prices this year, immediately hailed the announcement as "a major break-through" in the administration's anti-inflation campaign.

The 3 percent increase, if followed by other firms, would be the third price rise, totaling more than 95 percent, announced by the industry this year.

Although the nation's other major steel producers withheld comment on the Bethlehem announcement, Barry Bosworth, the director of the Council on Wage and Price Stability, predicted they "will have little choice" but to follow Bethlehem's lead. In the steel industry, the first price increase announced by one of the major firms generally sets an industrywide pattern.

Bosworth and special trade representative Robert S. Strauss, President Carter's chief inflation counsel, announced the Bethlehem decision at the White House. They said that by raising prices only 3 percent the rest of this year the steel industry would meet Carter's anti-inflation goals.

That interpretation was disputed even within the administration, however, because it excludes an increase by industry as a result of last winter's coal strike settlement.

When he announced the anti-inflation program, Carter said he hoped to hold usage and price increases this year below the average increase for each industry in 1976-77. The steel industry's target is less than 8.5 percent, according to Bosworth.

The industry prices by an average of 5.5 percent last February and March. On April 1, it followed with the equivalent of a 1.1 percent increase because of the Coal strike settlement and higher coal prices.

Administration officials conceded in private that when Bethlem's 3 percent is added to the earlier increases the industry has techincally exceeded Carter's anti-inflation goals. But they argued that given the special burdens of the steel industry, Bethlehem's decision amounted to a show of restraint justifying the ballyhoo Strauss and Bosworth attached to it.

"On a literal interpretation, we did not get (price) deceleration, but frankly, we expected a hell of a lot more in price increases then we got this year," one government analyst said.

The analyst said it is quite possible that under the Bethlehem pattern the steel industry will not fully recover its cost increase this year.

"At the start of the year, we knew steel was one of our trouble areas," he said. "There was the prospect of rapidly rising costs, low profitability and huge enviromental outlays. We were very dubious about our prospects of getting restraint.

"In view of our expectations, to get them even on a plateau is something we're happy about."

Bosworth told reporters he thought the steel industry had met the president's anti-inflation goal. But he said he had "discounted" the earlier 1.1 percent price increase that followed the coal strike settlement. He also said that the industry's February and March price increases were not "across the board" and totaled slightly less than 5.5 percent rise that was announced.

The coal strike settlement involved a wage and fringe benefit package that is expected to boost labor costs by as much as 39 percent over the next three years. Administration officials said that because the steel industry will have to absorb much of this in the form of higher coal prices there was justification for Bosworth to discount the steel industry's 1.1 percnet price increase in April.

Strauss, the administration's chief anti-inflation salesman, seemed less interested in the details of the numbers than in seeking to use the Bethlehem decision for maximum psychological leverage in dealing with other industries.

He called Bethlehem's announcement "probably the most substantive step we've taken in the anti-inflation effort" and an example of "corporate good citizenship," A few weeks ago, he said, some steel executives were talking about a possible increase of 7 percent.

But Strauss said he pressed Bethlehem executives to accept 3 percent, adding that he hoped their decision "might turn the tide" against the continuing rise in prices and wages. He said, however, he had pledged nothing in return for the industry restraint.