President Carter and U.S. Steel Corp. clashed openly yesterday over the latest steel price increase, with indications that the industry may settle for a smaller amount than the $10.50 a ton that U.S. Steel announced on Wednesday.

At a news conference in Caracas, Venezuela, Carter blasted U.S. Steel's announced increase as unjustified, contending it "fits in very poorly" with the administration's anti-inflation goals. The White House says the increase is larger than is needed to offset the higher costs of the new nationwide coal contract.

A few hours later, National Steel Corp., the third largest steelmaker, announced a price increase of $5.50 a ton - about half U.S. Steel's - but warned it may have to raise its prices further later.

The White House praised National for moderation.

In a surprise development, U.S. Steel said it would be willing to discuss the increase with administration wage-price officials.

David M. Roderick, the company's president, told an audience in Chicago that "if the president asks us to roll back, we would certainly listen to the president." However, he noted, "we haven't announced a price increase to roll it back."

The industry's response yesterday was regarded as significant. It marked the first time the major steel makers have softened their stand on a price rise since Carter took office. Last summer an administration attempt at jawboning was met with open defiance.

The average price of a ton of steel now is $477, according to U.S. Steel.

The developments came as, separately, administration economic officials put the finishing touches on a new anti-inflation program to be submitted for Carter's approval on Tuesday.

Carter in Caracas said, without elaborating, "When I get home, one of my first actions will be to make public" new anti-inflation proposals.

Although details could be changed before next week, the major element is expected to be imposition of a 5 to 6 percent ceiling on new federal pay increases this year, instead of the 7 percent hike that most likely would result otherwise.

This, an official said, would "provide a visible demonstration that the government is getting its own house in order" before asking business and labor to scale down their wage and price demands, as Carter called for in January.

The White House also is expected to propose other steps - including opening more federal timberlands to cutting to reduce lumber prices, and increasing pressure on specific industries to take steps that would slow inflation. However, all of these are being described as modest.

The outcome of the White House dispute with the steel industry now depends largely on reaction by Bethlehem Steel Co., the second largest. Analysts say if Bethlehem goes along with the smaller $5.50 price rise, U.S. Steel, the largest producer, will be forced to roll back.

Following the president's comments yesterday, officials of the Council on Wage and Price Stability, the administration's inflation watchdog, began contacting Bethlehem and other steel producers to urge them to stick to the more moderate price increase.

Jack Meyer, assistant director of the council, said the administration was "very pleased" that National Steel had proposed a smaller increase than U.S. Steel. He said the action "reflects concern" by National "for the country's inflation problem."

Carter's remarks in Caracas were accompanied by bristly language from administration officials.

In a speech in Mount Clemens, Mich., Vice President Mondale called the U.S. Steel increase out of line and expressed hope that "they'll change their mind."

Charles L. Schultze, chairman of Carter's Council of Economic Advisers, told an audience in Indianapolis that the administration "does not intend to let inflation get out of hand" because "the adverse consequences for our economy would be much too serious."

The administration has stiffened its anti-inflation stance in recent days under increasing pressure for stronger wage-price action. Until the past two weeks, critics had charged the White House was doing virtually nothing to deal with the price situation.

The steel price developments came as the government published new figures showing the economy has weathered the coal strike in good shape. The Commerce Department reported new factory orders rose a sharp 3.8 percent in February. And other government indexes showed no major damage.

Describing the anti-inflation program the administration is drafting, officials stressed that Carter has not finally approved any of the major elements being considered. But he has given the go-ahead for initial "consultations" over the federal pay holddown - the first step toward firm action.

Leaders of federal employe unions have complained that the pay ceiling would unfairly by take more away from government workers than from those in the private sector. However, White House officials pointed out that Civil Service workers aren't affected by Social Security payroll tax increases.

Officials say they also are fairly certain Carter will approve their plan to open federal timberlands to increased cutting by private companies, to help drive down lumber prices. One source said the only hitch will be to convince environmentalists that the move would not devastate forests.

In the steel-pricing dispute, the administration and the steel makers have been at odds over how big a price boost is necessary to cover increased coal costs resulting from the recent 39 percent wage hike in the miners' three-year contract settlement.

The Council on Wage and Price Stability estimates the boost at $3.50 or so rather than $5.50 to $10.50 a ton.