Credit demand will grow by a record $412 billion in 1981, a third more than it grew this year, and interest rates will remain near their historically high levels, according to Henry Kaufman, chief economist for the investment banking firm Salomon Brothers.

Kaufman told reporters that interest rates, already near the record levels they hit last spring, will go even higher before they turn down again. "But how high is high? It's difficult to say," he said.

Kaufman, whose utterances on interest rates and the bond markets are closely watched by Wall Street investors, painted a dismal picture for the economy and credit markets next year.

Kaufman said that the incoming Reagan administration's desires both to cut taxes and sharply raise defense spending will hurt both inflation and the interest rate situation.

He said that interest rates will not fall sharply early next year as they did this spring. After the prime rate touched 20 percent in early April, it began a steady decline that ended at 10 3/4 percent last summer. Rates quickly began to climb again. Last Friday the prime lending rate hit 19 percent, and analysts expect it again to hit 20 percent within a matter of days because the Federal Reserve Board is riding hard on monetary policy in an attempt to fight inflation.

He noted that a year ago the economy was working at full speed so that when economic output began to slide, some of the pressure on interest rates was reduced. Today, however, the economy is far from full employment. Furthermore, he said, the slide in interest rates last spring was "detonated" by the imposition of credit controls by the president last March.

"Such an action is unlikely this year," he said.

Kaufman said that interest rates probably will be as volatile as they were this year. He said that after rates peak, probably some time in the first three months of the year, they will decline but that the decline will end abruptly when companies jump in to sell their long-term bonds.

Kaufman said that the economy will recover very slowly in 1981 and might not grow at all during the early months of the year. But inflation will remain high as workers push for bigger wage settlements to help them catch up with inflation, oil producers continue to raise their prices, food costs jump as much as 15 percent (compared with 8 percent this year) and high interest rates add to the cost of doing business.

Normally, at the end of a recession businesses "gain a respite from" the need to borrow and instead pay off some of their short-term loans. But if the economy behaves as predicted, Kaufman said, "even a brief respite is unlikely in 1981."

"We expect that total external financing requirements will rise from this past year's estimated $106.3 billion to $125.5 billion in the coming year -- an 18.1 percent jump versus the precipitous fall in the first years of the last recovery period." During 1975 and 1976 corporate borrowing declined 42.9 percent.