Federal Reserve Board Chairman Paul A. Volcker yesterday publicly praised for the first time a compromise between President Reagan and Republican congressional leaders to reduce the federal budget deficit, saying such a program is essential to solving the nation's economic problems.

However, Volcker also expressed concern that the nation's goods-producing sectors were being left out of the current economic expansion and that such an imbalance could hurt future economic growth.

"I can't help but be encouraged by the steps that were announced last week by the Senate Republican leadership and the administration," Volcker said. "I'm no expert on all their calculations and all their details, but on the face of it, it seems to me the order of magnitude they're talking about, the timing of what they're talking about seems to be appropriate to the situation."

Volcker said attacking the deficit "doesn't mean it's easy politically" or in nonpolitical ways. "You have continuity of programs. You have other priorities," Volcker said. "It's always an enormous problem to change the direction of this great engine of government."

Volcker said he also knows that there is quite a distance between an agreement in principal and actual enactment of such a program. He added that it is necessary to "build up an opinion among the public at large that this kind of program really is essential to our fundamental economic problems."

The plan adopted by the president and Senate Republicans would reduce the budget deficits from more than $200 billion a year to less than $100 billion each year by fiscal 1988. The deficit would be cut next year by $52.1 billion to $175.3 billion.

"It's becoming more obvious that important sectors of the economy are being left out" of the current expansion, Volcker said. "Sectors like mining, manufacturing and agriculture. When I say mining, manufacturing and agriculture . . . it's the whole goods producing area. It is no longer even half the economy, but it is a very important part of the economy in a number of dimensions," such as producing exports and competing with imports.

Volcker said the industrial production index has been flat for almost nine months, and that employment in the manufacturing industry has not grown in recent months. At the same time employment in services has increased, as it has in construction, to some degree, "but not in manufacturing, not in agriculture and not in mining," he said.

Such an economic imbalance leads to a series of questions, Volcker said, such as, "How strongly, how long can growth be maintained in the American economy under these conditions? Indeed at this point I think it is a relevant question -- with the continuing flatness of production -- as to whether to some degree investment plans, which so far have been quite strong, will begin to be reevaluated."

Related questions raised are what the imbalance means for the prospects of growth abroad and the long-term implications for sectors involved in trade, Volcker said.

In response to questions, Volcker said the recent problems of two government securities dealers "are a matter of concern" to the Fed, but he said he didn't have any proposals on how to deal with it.

This week a New Jersey government securities dealer filed for bankruptcy and last month the failure of E.S.M. Government Securities Inc. caused $315 million of losses across the nation and resulted in a run on privately insured savings and loans associations in Ohio.