The nation's major banks boosted their prime lending rate to a record 19 1/2 percent yesterday as trading markets began to stabilize after a day of panic.

The prime -- the rate banks charge on loans to their most credit-worthy corporate customers -- stood at 19 percent before the latest series of increases. As recently as one month ago, the prime lending rate was 16 3/4.

Gold and silver prices, in the meantime, began to recover from the panic that hit the commodities markets Thursday. Prices for both gold and silver rose sharply with gold closing in New York at $509 an ounce, up $46 from Thursday.

Silver prices closed at $13.25 in New York after dropping as low as $10 the previous day.

The stock market also rebounded sharply from Thursday's chaos. The Dow Jones Industrial Average closed up 17.66 points on moderate trading.

The latest boost in the prime rate was triggered by Citibank in New York.

Citibank raised its prime from 19 to 19 1/4. But other major banks quickly raised their rate to 19 1/2. By the end of the day most major banks has boosted the rate to 19 1/2.

The increase was the seventh during March and the 13th in 1980. Rates have shot upward as the government has tightened credit as a means of fighting inflation and slowing the economy.

"It's a logical reaction to the rising cost of funds," said Donald Maude, chief financial economist at Merril Lynch & Co.

The 19 percent rate -- a record at the time -- was first charged March 19.In mid-February, the rate was 15 1/4 percent, but it began moving up sharply after the Federal Reserve Board again tightened credit in mid-March.

The new increases make it even more expensive for businesses to raise cash, and some economists predicted yesterday the demand for corporate loans will begin to slow soon.

"Demands are still strong now, but by mid-April I think we'll see a softening of demand," said David Jones, an analyst at Aurbey G. Lanston & Co. in New York. "There's likely to be a sharp drop-off in loan growth." &

The dollar was narrowly mixed against major currencies yesterday, gaining against the West German mark and the French franc but falling against the Swiss and British currencies.

Currency dealers said high interest rates once again helped support the dollar, even in the face of Thursday's announcement of a record $5.6 billion U.S. trade deficit in February.

In New York, dealers said most of the dollar's gains came while European markets were still open. Trading, while fairly active at mid-morning, tapered off later in the day, a New York dealer said. Concern about commodity markets had little effect on dollar trading, he said.

The dollar's climb against the West German mark brought it to its highest level in Frankfurt since December 1978. It reached its highest level in four years against the Italian lira.

Late dollar rates in European centers, compared with late rates Thursday and with last Friday's late rates in parentheses were : Frankfurt, 1.9270 West German marks, up from 1.9225, (1.8775); Zurich 1.8255 Swiss francs, down from 1.82625, (1.77775); Paris, 4.4510 French francs, up from 4.42825, (4.3700); Amsterdam, 2.1065 Dutch guilders, up from 2.1015, (2.0570); and Milan, 893.05 Italian lire, up from 888.40, (873.75).

The British pound edged ahead in London to wind up at $2.1750 compared with $2.1735 Thursday, but down from $2.1815 at the end of last week's trading.

In Tokyo, where the business day ends before Europe's begins, the dollar closed at 249.775 yen, up from 249.625 yen Thursday and 249.15 last Friday.

Dollar rates, as of 4 p.m. in New York included: 1.9315 West German marks, up from 1.9248; 4.4588 French francs, up from 4.4393; 1.8818 Swiss francs, down from 1.8343; 249.40 Japanese yen, down from 249.92; 1.1878 Canadian dollars, up from 1.1861. The British pound rose to $2.1770 from $2.1705 Thursday.