Stock and bond prices collapsed today on apparent investor concern that the record deficits proposed in the Reagan administration's new budget will push interest rates higher.

The Dow Jones Industrial Average fell 17.6 points to 833.43, its lowest level since Sept. 25, when it hit 824.01. On the New York Stock Exchange only 273 stocks closed higher in price while 1,330 declined.

Bond prices tumbled, too. Higher interest rates mean lower prices for bonds, whose interest payment normally are fixed for the life of the security. Andrew Morse, of the brokerage firm Drexel Burnham Lambert Inc., said bond prices declined about $20 for each $1,000 of face value.

Morse said, however, that it is difficult to understand why either the stock or the bond market declined so precipitously. It had been expected that the president would refuse to budge from his campaign position of increasing defense spending and lowering taxes in order to stimulate noninflationary economic growth.

"I know no more today than I did Friday," Morse said. "Reagan is sticking to his campaign guns. I'm surprised the market is so offput."

"Offput" it was, however. Early declines in bond prices, which have the result of raising the interest yield on those bonds, immediately spilled over to the stock market.

The Dow average was off more than 8 points within the first half hour of trading, rallied briefly just before noon, then began a steady decline that accelerated in the final minutes before the 4 p.m. closing bell.

Today's decline was not sparked by a heavy surge of panic selling, however. Rather prices declined because of a dearth of buyers willing to gamble that stock prices would rise in the near future.

"The markets are plagued by uncertainty," said one analyst. "We know that Congress will ultimately reshape the budget. But that's six months or more down the road. Investors just don't like uncertainty."

"Since early December there's been a buyers' strike," said Larry Wachtel of the brokerage firm Bache Halsey Stuart Shields Inc. Usually, he said, once a decline begins, there are groups who step in at various points to buy stocks at bargain prices. Only a few times in the past two months have there been such "technical" rallies in stock prices.

"When the buyers come back, we have 72-million-share days. When they're not there, we have 48-million-share days," Wachtel said. Today was a 49.3-million-share day on the New York Stock Exchange.

The New York Stock Exchange's own index was off 1.47 points to 66.32. On the American Stock Exchange the index fell 8.26 points to 277.25.