Most of the nation's major banks raised their prime leading rate to a record 17 1/4 percent today, as short-term interest rates continue to skyrocket because of inflation, strong demands for funds and a tightening Federal Reserve monetary policy.

Prices in both the stock and bond markets fell sharply on news that Chase Manhattan Bank had initiated another round of prime-rate increases.

But stock prices recovered near the end of the day, and bond prices regained some of the ground they lost. The Dow Jones average of 30 industrial stocks, which was down more than 7 points earlier in the day, closed up 2.13 to 856.48. But the Dow's broader based list of 65 stocks closed down 0.27 point at 313.95.

Over in the bond market, where prices have been falling and yields rising since the first of the year, prices were down about $20 (off a face value of $1,000) early in the day, but recovered about $5 of that near the end. v

Reports in major newspapers that the administration has decided not to impose credit controls as part of an anticipated new anti-inflation strategy also helped to send bond prices tumbling.

Although economic controls of any kind are anathema to most business executives, many beleaguered bond traders want credit controls to slow the growing demand for loans that has pushed short-term interest rates above 17 percent.

The Treasury, whose securities are considered virtually risk-free, had to pay 15,296 percent today on a sale of $4 billion of 43-day bills, a record. Federal National Mortgage Association had to pay a record 15,356 percent on its auction of four-month commitments to buy home loans.

Peter Treadway, chief economist for the FNMA, said the bids were received on Monday and they "do not reflect the further deterioration (in bond prices) today." Treadway said that with mortgage rates now well above 15 percent, "A great many potential borrowers cannot qualify for mortgage loans."

The half-point jump in the prime lending rate -- the interest the best heeled corporations pay for short-term loans -- followed a similar leap last Friday from 16 percent to 16 3/4 percent.

Banks now are paying more than 16 percent for certificates of deposit -- large deposits left with the bank for a specific period of time. Because banks have to set aside a percentage of those funds to satisfy federal Reserve Board requirements, the money is costing banks 8 percent or more.

"We're looking at a prime rate of 18 1/2 percent or better by late spring," said Leon Gould, an economist at Commercial Credit Corp.

Even as short-term interest rates rise to levels thought impossible even months ago, business demand for loans continues strong.

Bankers report that their corporate customers and other borrowers are trying to set up lines of credit in anticipation of credit controls and that many borrowers are turning to banks rather than trying to sell their own securities in the chaotic bond markets.

Even giant Citicorp, parent of New York's biggest bank, called off its planned sale of $250 million in notes because of market conditions.

The only salutary development in the interest-rate front today occurred abroad. The dollar's value rose sharply in Europe because of the rise in the prime rate.

Volume on the Big Board was heavy. Nearly 44.6 million shares of stock changed hands today compared with 38.7 million shares Monday. The New York Stock Exchange index of common stocks was up 0.01 point to 64.36.

But prices of stocks whose companies are sensitive to higher interest rates -- such as finance companies or utilities -- declined. The NYSE utilities index was down 0.35 point, while the finance index was off 0.33 point.

Oil company stocks, which declined in early trading, rebounded near the end to help push the Dow average up 2.13 points.

The American Stock Exchange index was off 1.22 points to 300.16, with 450 issues declining and 166 rising.

Nearly all Treasury notes and bonds declined in price today. The Pacific Telephone Co. bonds issued last week declined $7.50. But because these bonds were sold just before a small rally in bond prices last week, they still are selling above face value.