In a step immediately endorsed by the White House, the Federal Reserve Board yesterday boosted the discount rate from 7 1/4 to 7 3/4 percent in an effort to bolster the sagging dollar and help counter domestic inflation.

The discount rate is charged member banks that borrow from the Federal Reserve. The decision to raise it does not necessarily mean other interest rates will also rise; the Fed was mainly catching up with the market, where short-term interest rates already are over 8 percent.

But the Fed's action has symbolic importance for the troubled dollar, and the administration's prompt expression of approval signifies president Carter's willingness to risk a dampening of the domestic economy for international and anti-inflation reasons.

Higher interest rates work against inflation by discouraging business borrowing and reducing general economic demands, but in that same process they also reduce economic growth. They help the dollar - in theory at least - by giving dollar-holders added incentive to hold onto their money.

It was only the sixth time in the past 15 years - and possibly longer - that the discount rate was increased for international reasons. (Prior to 1963, the board's press releases did not specify reasons for changes in the discount rate.)

The last such occasion was in January, when, under the direction of then-chairman Arthur F. Burns, the Fed raised the discount rate - to the surprise and discomfort of the Carter administration - from 6.0 to 6.5 percent.

In a statement issued yesterday by press secretary Jody Powell, the White House this time said it "fully understands" the reasons for the Fed action, and added: "It is essential that we control inflation if we are to have a strong dollar and sustainable economic growth."

The seriousness of the inflation problem was underscored by a revised Commerce Department estimate of gross national product for the second quarter. The 10.1 percent inflation rate first reported was raised to 10.7 percent. And although the gain in real GNP was upped to an annual rate of 8 percent from the first estimate of 7.4 percent, it was still far behind earlier anticipations. (Details on Page C8.)

Financial market observers welcomed the increase in the discount rate, which they had anticipated. But they were far from effusive. "This will help the dollar a little bit, temporarily," said economist Henry Kaufman of Salomon Bros., New York. "But there's got to be a lot more."

Traders said that exchange market activity was almost nonexistent from noon on, although final quotations showed the dollar up against all major currencies. The markets, according to one expert, expect fresh news over the weekend, although officials here indicate nothing is planned.

Beyond the actual discount rate increase itself, financial men were pleased by the prompt White House approval."Whether they're happy or not," said one observer, "at least they're getting their act together.."

An administration source said yesterday that the Fed's increase in the discount rate - now at its highest level in 3 1/2 years - "should be viewed as the first in a series of actions that will be announced from time to time over the next few weeks to deal with the dollars."

Under the direction of Treasury Secretary W. Michael Blumenthal and Fed Chairman G. William Miller, officials are trying to pull together a program that will restore a sense of confidence in the dollar.

Possibilities under discussion, to supplement higher interest rates, include the assembly of greater resources of hard currencies for intervention in currency markets to prop up the dollar. The basic policy of intervening only to modulate "disordely" markets would be continued.

But the policy might have more credibility if the available funds were beefed up. The United States could borrow from the International Monefund, or sell more gold to obtain more currencies.

Reducing energy imports as a way of lowering the overall trade deficit remains a high-priority objective, and administration officials were cheered by a compromise on natural gas price deregulation, which will at least get a bill to Senate and House floors.

Another possible element in the administration's dollar support program could be acceleration of export-stimulus incentives, under study for months at the Commerce Department.

Ways of improving the anti-inflation program without worrying both business and labor about the prospect of formal wage-price controls are also being re-examined.

But for the moment, the dollar-support program rests heavily on a tighter-money policy, which had been resisted until now by administration spokesmen such as Council of Economic Advisers Chairman Charles L. Schultze.

Most economic forecasts, including the CEA's suggest that economic growth in 1979 will slide below the 4 percent target generally considered to be the minimum acceptable level. Under a 3.5 to 4.0 percent growth range, economists say, unemployment tends to increase.

With sluggishness lying ahead, both the administration and Miller had said publicly they hoped that interest rates would be topping out this fall, and declining next year.

Because of the plight of the dollar, Miller appears to have changed his course, and the Carter administration concluded that it had no options without risking a dollar collapse. "We don't always have our druthers," an administration official sighed.

But the increase of the discount rate to a level below 8 percent is clearly following, rather than leading the market, especially in view of an increase yesterday in the federal funds rate target from 8 to 8 1/2 per-

The federal funds rate - the one at which banks borrow from each other - is the basic determinant of short-term interest rates. It is established by Fed actions in the Securities markets. Dollar-watchers would have been happier if the discount rate had been boosted all the way to 8 percent, because that would have been a true indication that international, rather than domestic considerations were getting priority in the Fed's decision-making process.

Technically, the Fed merely approved the petition of 11 of the 12 member banks for a boost in the discount rate they charge. Later, Dallas, the 12th district, joined in as well. It was the fourth discount rate increases so far this year.