Most major steel producers bowed to heavy administration pressure yesterday and announced price increases that undercut the $10.50 a-ton boost announced by industry giant U.S. Steel Corp. last Wednesday.

President Carter had denounced the increase as inflationary and said it did not fit in with the anti-inflation program he had announced.

Bethlehem Steel Corp., the nation's second biggest steel maker, announced that it would raise prices $5.50 a ton, effective today, to cover the increased costs of the nationwide coal pact.

Bethlehem followed the lead taken Thursday by National Steel, the third biggest producer. Other steel companies announcing the smaller increase yesterday were Republic, Inland and LTV Corp.'s Jones & Laughlin.

The $10.50 increase announced by U.S. Steel, which the company said was equivalent to a 2.2 percent increase on average, came at a crucial time for policy makers because inflation has become of increasing concern.

The President has been under pressure from economic aides to take actions to hold inflation and the President said Thursday in Brasilia that he will announce an anti-inflation program when he gets back from a trip to South America and Africa next week.

When U.S. Steel announced the $10.50 increase, the White House Council on Wage and Price Stability issued a statement saying that all the company could justify as a result of the coal settlement was $4 a ton.

But a spokesman for the council said yesterday the agency is "pleased" with the $5.50 a ton most producers have announced.

The council spokesman said that when the indirect costs of the nationwide coal pact, such as higher electricity rates, steel producers can be expected to incur cost increases of about $5.50 a ton.

US Steel, which was scheduled to put its higher pric increase into effect today, had no comment yesterday, although industry analysts said the smaller price increases posted by Bethlehem, National, Inland, Republic and J&L. Only Wheeling-Pittsburgh, the ninth-biggest producer, matched the U.S. Steel lead.

Bethlehem's announcement was terse and took no notice of government concern. Bethelehem said simply that the $5.50 would cover the "minimum estimated cost" of the coal pact "cannot be absorbed" and will have to be "reflected in future price adjustments."

But other steel companies took note of the need to fight inflation. George Stinson, chairman of National Steel Corp., said Thursday that he felt an increase bigger than $5.50 would have adverse consequences on the overall fight against inflation.

Economists estimated that the $10.50 boost would add between $10 and $15 to the cost of a new car, while the $5.50 boost would add about half that.

But steel is such a widely used product, that price increases in that sector have psychological consequences that go beyond the direct impact cost impact of a price increase.

Some economists and administration officials are worried that the current atmosphere could trigger anticipatory wage and price increases that would become self-fulfilling prophecies for inflation.

The price increases that take effect today follow a 5.5 percent raise that most companies put into place only last Feb. 1.

The Council on Wage and Price Stability, in a statement criticizing the U.S. Steel increase Wednesday, noted that if the steel industry is to cooperate with the President's program to knock a half percent off the inflation rate this year, then steel producers (and U.S. Steel in particular) will not be able to raise prices any more after this increase.

Steel prices rose 8.5 percent in 1977 and have risen between 6.5 percent and 7 percent already in 1978.

While nearly all steel companies talked of the need to increase prices further in the future to account for rising coal costs and other cost increases, none said when such increases would be required.

Many steel companies, including U.S. Steel, expect an unprofitable, or barely profitable, first quarter because of the coal strike. But orders are up substantially for the next few months, in part because of a pickup in steel demand and in apart because of a special government program designed to reduce steel imports.