The prime interest rate may reach 24 percent before peaking and heading downward, Henry Kaufman, chief economist of Salomon Brothers and an influential financial commentator said yesterday.

Last Friday, many major banks raised their prime rates -- the interest rates they charge their best corporate customers -- to 21 1/2 from 21.

In an interview on ABC's Issues and Answers, Kaufman said he does not expect a recession next year, but sees instead a drawn-out period of unususally weak economic growth and high inflation.

He predicted a year-to-year economic growth rate of only 1 1/2 percent in 1981 -- an extraordinarily low rate at a time when the country is coming out of a recession.

"All the signs suggest that we do not have the setting for a real, powerful economic recovery," he said.

These conditions add up to an economic emergency, and the country has been in one for some time, said Kaufman, whose economic analysis is closely watched by the financial markets and by government policy makers.

But it would be a mistake for President-elect Ronald Reagan to declare an economic emergency upon taking office next year, he added.

"Living in one is one thing, calling for the declaration of one is another," said Kaufman, joining the debate over the proposal by some of Reagan's advisers that the new president declare an emergency in order to mobilize action by Congress on a new economic policy early next year.

Both Treasury Secretary G. William Miller and Charles L. Schultze, chairman of President Carter's Council of Economic Advisers, have recently jumped on the proposal, calling it "dangerous" and irresponsible.

The danger with declaring such an emergency, said Kaufman, is that it requires draconian measures be introduced by Congress and by the president of the United States," he said.

Although Kaufman didn't elaborate, to some financial analysts, the term "emergency measures" spells firm governmental controls over prices, wages or credit, all of which would require congressional action and would trigger an intense legislative battle. Reagan advisers have never said they have such steps in mind, but the problem, said Kaufman, is that the country's financial and business communities would expect them once an emergency was declared.

And if such economic measures were not approved, Kaufman said, the failure would leave the business and financial communities jittery and confused, he explained.

It is critical for the Reagan administration to avoid falling into such a credibility gap on economic policy, said Kaufman.

To achieve credibility, the Reagan administration must push through impressive reductions in the growth of federal spending early next year, before completing action on tax cuts, Kaufman said.

"This administration [of Reagan's] must go very carefully into the uncontrollable expenditures, into the entitlement programs, into a variety of welfare programs, into a variety of social security programs . . . and has to say, we have to change. . . We have to make enormous changes," Kaufman said.

"Every president has talked about this. This president is going to have to perform on that issue," he said.

Predicting that inflation will be near the 11 percent rate by the end of next year, Kaufman said that the first positive impact the Reagan administration could have on the problem is psychological and emotional.

"Shackling the growth of federal expenditures" could help persuade the business and financial communities that the new administration is committed to reducing inflation, Kaufman said, and that would be a significant gain.