Chase Manhattan Bank raised its prime lending rate to a record 13 percent yesterday, just as President Carter was predicting that the nation's inflation rate will "go down the rest of the year."

Carter, answering questions from an audience of retired persons in Hartford, Conn., said that energy price increases should level off and the overall inflation rate should decline.

Chase's move in the opposite direction, effective today, came only three days after it and other major banks had raised the prime interest rate from 12 1/4 percent to 12 3/4 percent. Other banks are expected to follow Chase's lead, and many leading analysts expect the prime rate to go even higher within the next few weeks.

A spokesman for the bank said Chase increased the rate, which it charges its best corporate customers for short-term loans, because business demand for loans remains strong and because the cost of funds the bank acquires to lend is rising sharply.

Interest rates have shot upward in the last month in large part because the Federal Reserve Board has been pursuing a tighter monetary policy since its new chairman, Paul Volcker, took over in mid-Agusut. Volcher has defended the high-interest-rate policy as necessary to break "inflationary expectations."

Many economists are worried that the Fed may be raising interest rates too far too fast with the economy already headed into a recession.

In Hartford, President Carter blamed most of this year's increase in inflation on higher energy prices, spurred by higher prices on crude oil by the Organization of Petroleum Exporting Countries. According to an analysis by his economic advisers, he said, if energy prices had not changed, the inflation rate this year would have been only fractionally higher than last year's rate.

But even without energy, this year's rate is nearly 10 percent, the Carter figures show.

"We do not anticipate -- although I cannot control this -- we do not anticipate any further increases by OPEC this year," Carter said. "So the rate of increase, even in energy, is likely to level off."

Later, Carter declared flatly, "I ex- pect the rate of inflation to go down the rest of the year."

Administration economists are counting on a lower rate of inflation to boost the purchasing power of workers' take-home pay, encourage consumer buying and bring the economy out of what they hope will be a shallow recession.

Continued increases in interest rates could end that prospect, some private economists warn. "The Fed is flirting with making the same mistakes it made in 1974," said Allen Sinai of Data Resources Inc., a major economic forecasting firm. That year, then-record interest rates helped bring on the nation's worst post-war recession.

Henry Kaufman, the respected chief economist of the Salomon Brothers investment banking firm, said he expects the prime rate to climb to 13 1/4 percent or 13 1/2 percent within the next three or four weeks, even if the Fed takes no further steps to tighten credit.

Kaufman said he doubts the Fed will back off, because "so far, there is no evidence that the willingness to lend or borrow has been affected by the increases in interest rates."

In line with that view, figures released yesterday by the Federal Reserve showed that business and industry loans at major U.S. banks rose $2.24 billion in the week that ended Sept. 5. At New York banks alone, such loans grew $1.1 billion.

By raising interest rates, the Fed is searching for a level that will discourage many borrowers from seeking loans.

Meanwhile, in a development that should keep American farm prices high, the Agriculture Department lowered its estimate of grain production in the Soviet Union this year to 180 million tons, 5 million tons less than was forecast last month.

At the same time, the department raised its forecast for the U.S. corn crop to 7.27 billion bushels from the 7.1 billion predicted last month. The estimate for the wheat crop was revised downward slightly to 2.12 billion bushels, and the soybean crop was pegged at a record 2.17 billion bushels.