The Federal Reserve Board lowered a key lending rate yesterday as signs mounted that the nation's economy is caught in a recession and market interest rates are falling.

Producer prices for finished goods, many of which are highly sensitive to the health of the economy, rose a seasonally adjusted 0.2 percent in September, the smallest monthly increase in more than three years.

At the latest auction of 13-week Treasury bills, yields fell to 13.526 percent from 14.206 percent at the auction Monday. It was the lowest rate since June 15.

With a wide range of interest rates declining, as a result of both a weaker economy and decisions by the Federal Reserve, the administration cut the maximum allowable interest rate for mortgages insured by the Federal Home Administration and the Veterans' Administration by one percentage point. The top rate for level-payment mortgages on single-family homes will drop Monday from 17.5 percent to 16.5 percent.

The Fed, whose current policy stance was criticized earlier this week by Treasury Secretary Donald T. Regan, lowered from 17 to 16 percent the interest rate it charges on loans to large financial institutions that borrow frequently from it. The central bank's basic rate of 14 percent charged most borrowers was left unchanged.

In a statement, the Federal Reserve said the action was "a further technical response to the decline over recent weeks in short-term money market rates." The board emphasized that the action was "taken within the context of the continuing policy to restrain growth in money and credit."

Another decline in the level of the most closely watched measure of the money supply, reported yesterday by the Fed, provided additional evidence of the effectiveness of that restraint.

Analysts said the drop of $1.9 billion for the week ended Sept. 30 in M1-B, which includes currency in circulation and checking deposits at financial institutions, was also a reflection of growing weakness in the economy.

A growing number of forecasters believe that the economy currently is contracting for the third quarter in a row, and a minority of them expect the declines to reach well into next year. If these forecasters are correct, this period probably will be labeled a recession when final data are available.

Meanwhile, in Hot Springs, Va., at a meeting of the Business Council, an organization of corporate chief executives, Walter Wriston, chairman of Citibank, the nation's second largest bank, predicted that the prime lending rate at major banks, now 18 1/2 or 19 percent, would fall to between 9 and l0 percent by the end of next year.

Statements by administration officials in Washington and by others attending the Hot Springs meeting added to the confusion over exactly how the Reagan administration feels about Federal Reserve policy.

Vice President Bush said at the National Press Club here that the administration believes the Fed "is doing the right thing." Bush said, "We're not going to go out and attack the Fed for doing that which it was criticized for not doing earlier. The administration feels the Fed, in trying to control the growth of the money supply, is doing the right thing."

However, Regan and presidential counselor Edwin Meese III told reporters in Hot Springs that the Federal Reserve may be restricting money growth more than is necessary. "In recent weeks the money supply has less than 2 percent growth," and that is not fast enough, Regan said.

Meese said Regan had President Reagan's blessing to try to persuade the Fed to ease credit conditions more rapidly.

Both men said the difference over monetary policy was not just with Federal Reserve Chairman Paul Volcker but with the entire Fed board.

"I would say there is a great deal of agreement between Donald Regan and Paul Volcker," Meese said, "but that agreement is not always shared by the other members of the Fed."

The statements by Regan and Meese left analysts more puzzled than ever. The Fed, after the usual one-month delay, released the minutes of the August meeting of the Federal Open Market Committee, which sets Fed monetary policy.

At that meeting, the FOMC, including Volcker, voted as it had the previous month to try to boost M1-B growth to a 7 percent annual rate for the June-September quarter.

On the price front, the Labor Department said the consumer foods portion of the finished goods index was unchanged from August to September, as was the index for capital equipment.

The index for intermediate goods rose 0.1 percent, and that for crude goods fell 1.1 percent, the department reported. The foods and feeds component of both of those indexes declined sharply, raising the prospect that food prices may rise only modestly at least until the end of the year.

The 0.2 percent increase in finished goods prices would have been a much larger 0.7 percent except for the large rebates that auto and truck manfacturers paid to help sell the remainder of their 1981 models. Gasoline and heating oil prices continued to fall but by much less than in other recent months.