Interest rates soared, and the stock market plunged yesterday as jittery financial markets continued to react to the Federal Reserve's recent moves to tighten credit.

Several major banks boosted their prime lending rate a full percentage point to 14.5 percent, the largest onetime increase in history. The prime is the rate banks charge their best commercial customers. Other short-term rates rose as much as 1.5 percentage points yesterday.

As interest rates rose, the DowJones Industrial Average plummeted 26.45 points, following a drop of 13.57 points on Monday. Trading at the New York Stock Exchange was the fifth heaviest in history.

Financial analysts said the Fed's actions, announced Saturday, will soon lead to a squeeze on consumer and small-business borrowing, sharply restricted home mortgage lending and a slowdown in commercial construction. A more serious recession is now considered likely, economists said.

On international markets, the dollar continued to gain strength, but gold prices rebounded from Monday's decline to close at $391.50.

In the face of yesterday's financial news, President Carter reiterated his determination to fight inflation as the "number one threat to our economy."

Carter, at a press conference, said he believed his economic policy was sound and said he would maintain it even if that hurts him politically.

"Whatever it takes to control it [inflation], I will do," he said.

Federal Reserve Chairman Paul Volcker who engineered the sweeping changes in monetary policy that led to yesterday's interest rate surge, told a meeting of the American Bankers Association in New Orleans that the purpose of the measures is "to deal forcefully and responsibly with the economic and financial situation as we see it."

That situation, Volcker said, includes "strong inflationary pressures, concern . . . that excessive growth in money and credit might be permitted by the Federal Reserve fueling still more inflation, and an emerging speculative atmosphere and unsettled markets . . . ."

The Fed steps included changes in its methods of intervening in financial markets to try to control more directly changes in the level of bank reserves. Reserves are the portion of deposits that must be set aside before loans can be made. In the past, the Fed has tried to control reserves, and hence the amount of lending activity, indirectly by influencing the interest rate charged when one bank borrowed reserves from another.

"None of these actions will prevent moderate growth in money and credit commensurate with the needs of the economy," Volcker assured the bankers. "They are designed to curb excesses that would otherwise spill over into inflation."

The key to just how much the new policy approach will hurt the economy in the short run will depend in large part on whether interest rates remain high for an extended period.

Another element of uncertainty grows out of the move to control bank reserves. The Fed previously tried to control the level of bank reserves by concentration on interest rates partly out of a fear that freely and perhaps sharply fluctuating rates could by themselves damage the economy.

Yesterday's jump in rates was in response both to the Fed's announced increase in the discount rate -- the rate it charges on loans to its member banks -- and to this note of uncertaintyintroduced by the shift in policy on bank reserves.

Willard Butcher, president of Chase Manhattan Bank, for instance, said in New Orleans that he would not be surprised to see some banks moving their prime rates as often as twice a day, possibly boosting it in one move and lowering it in another.

But for now, interest rates are moving up, whatever downward fluctuations may come in the future. One sector of the economy that will be hurt is homebuilding.

Despite the use of a wide variety of new sources of lendable funds, savings and loan associations and other thrift institutions are beginning to run short of mortgage money. Savers already were getting higher yields elsewhere in the money market, and the Fed's steps have worsened this problem for the thrifts.

Deposites at mutual savings banks have been shrinking for some time, and preliminary figures indicate the nation's savings and loan associations suffered a loss of savings in September.

Kenneth Biederman, chief economist for the Federal Home Loan Bank Board, said savings and loans will have no choice but to cut down on their mortgage commitments because of the reduced savings flows.

Biederman, who had been predicting that the level of housing starts would fall from the August rate of 1.8 million units annually to about 1.5 million by the end of the year, is not sure higher interest rates will lower that figure further. However, he now expects a slower recovery for the housing industry in 1980.

Chase Manhattan, the nation's third largest bank, led the parade of big banks increasing their prime rates to 14 1/2 percent yesterday. The rate has jumped 2 1/2 percentage points in the last two months.

Since most business borrowers do not qualify for loans at the prime rate, they may pay several percentage points more. Moreover, many borrowers are required to keep a portion of their loan proceeds on deposit at the lending bank, and that raises their actual interest cost even more.

As it usually does, the stock market moved down in response to the higher interest rates. The Dow-Jones Industrials closed at 857.10, off 26.45 for the day. That is the average's lowest level since early August.

Many economists predict that the economy will decline in coming months, partly as a result of the Fed'stightening. Several say unemployment, which was 5.8 percent in September, will rise to 8 percent or perhaps more by late 1980.

Even if they agree that a recession of that magnitude is on the way, there is wide disagreement over just how much the recession will reduce inflation. For one thing, as President Carter noted at his news conference, energy prices are one of the driving forces behind inflation.

Whatever happens to the inflation rate, Fed Chairman Volcker hopes that world financial markets will not misinterpret U.S. monetary policy as the economy declines.

Since the Fed no longer intends to peg interest rates a drop in loan demand could mean lower rates in the markets even though there is no change in the target for the level of bank reserves, and no lessening of the Fed's resolve to fight inflation.

"When the money supply is brought clearly under control and expectations of inflation dissipate," Volcker told the ABA, "interest rates will tend to decline . . . . Developments of this sort are in no sense inconsistent with maintaining the firm discipline on federal spending and growth in the money supply that will be required over a long period of time to restore price stability."