United States Steel Corp. gave ground to the White House yesterday and rescinded the $10.50-a-ton price increase it announced last week - presumably in favor of a $5.50 increase imposed by other major steelmakers.

The announcement constituted a partial victory for the Carter administration, which had protested the $10.50 increase as unjustified. A spokesman for the Council on Wage and Price Stability called that agency "pleased" by the U.S. Steel action.

But the $5.50 a ton was still substantially higher than the $4 increase the council had said would be justified by higher labor costs from the new nationwide coal contract. Some analysts contend even the $5.50 is inflationary.

The U.S. Steel announcement followed a week of sparring between the White House and the steel industry.

U.S. Steel did not say specifically yesterday that it would go to $5.50. It said only that the $10.50 increase would be "modified to be competitive in the market on a product-by-product basis."

However, industry and government sources predicted that competition from other producers would force U.S. Steel to adhere to the $5.50 standard.A government analyst noted tersely that U.S. Steel "does not dominate" any one segment of the market.

The rollback by U.S. Steel was followed by a similar announcement from the other major steelmaker to propose a $10.50 increase, Wheeling-Pittsburgh Steel Corp. Like U.S. Steel, Wheeling-Pittsburgh did not specify the size of its new price increase.

The actions came as President Carter arrived home from his overseas trip apparently prepared to consider proposals for a new anti-inflation program - including a possible ceiling of 5 to 6 percent on federal pay increases.

The White House has been under pressure for some sort of symbolic action in the face of mounting inflation over the past two or three months. The anti-inflation program the president announced in January never has gotten off the ground.

However, it was not immediately clear when the president would announce the new program. Some aides hinted yesterday that despite his seeming eagerness in press conferences, Carter may wait until next week.

Besides the expected ceiling on federal pay increases, Carter is said to be considering opening up government timberland to more logging by private companies, to help reduce lumber prices. There are several other provisions along the same lines.

At the same time, the White House is expected to feel pressure from economic advisers, notably Secretary of the Treasury W. Michael Blumenthal, to begin acting more forcefully against inflation in day-to-day decisions.

Some critics note several actions in the past few weeks that have tended to exacerbate inflation. Among them are last week's decisions by the White House to buy more coopper to bolster prices, and to restrict imports of Citizens Band radios.

Carter advisers appear to be split over the anti-inflation program. Yesterday, Secretary of Labor Ray Marshall told reporters he would oppose any ceiling on federal pay increases unless it were part of a broad anti-inflation plan and done with consultations with unions.

Marshall said the president would have to make clear he expects the private sector as well as the government to hold the line on wages and prices.

Carter also has been urged by Blumenthal and Federal Reserve Board Chairman G. William Miller to act on his own if Congress doesn't pass the energy bill by May 1, and impose a $5-a-barrel fee on oil imports. They say it would help cut oil consumption here and bolster the flagging dollar.

Yesterday was the first time the Carter administration has won even minor concessions from the steel industry. Last summer, White House jawboning against a price increase met open defiance by the major steelmakers.

U.S. Steel is the nation's largest steel producer; Wheeling-Pittsburgh is ninth.

Separately, Armco Steel Corp. of Middletown, Ohio, announced it would join other steel producers in raising its prices by $5.50 a ton. The increases all are scheduled to take effect immediately.