First National Bank of Chicago, the nation's ninth biggest, today raised its prime lending rate from 11 1/2 to 11 3/4 percent as the brief respite in the upward climb of short-term interest rates comes to an end.

Several major banks including First Chicago, Chase Manhattan and Citibank -- lowered the prime rate in late January or early February, citing a decline in business loan demand and an easing in short-term interest rates.

As short-term rates on commercial paper declined, the cost to major banks of obtaining funds they relend declined.

But nearly all banks that cut their prime rate -- the interest charged their best corporate customers for shortterm loans -- warned that the decline was probably temporary.

Many major banks, such as First's giant Chicago rival, Continental Illinois, never cut their prime rate from the 11 3/4 percent level that prevailed throughout most of the industry from late December.

In another development, a group of leading monetary economists here warned the Federal Reserve Board that it must be careful not to step too hard on the growth of the money supply in its attempts to slow the rate of inflation.

By nearly all measurements, the growth of money has declined abruptly during the last four months.

The economists, members of a private group that gathers every six months to make recommendations to the Federal Reserve, conceded that measurement of the money supply is a chancy business these days because of changes in banking regulations and the way corporations manage their cash.

The Fed itself recognizes that its current definition of the money supply is outmoded and put out proposed revisions in January and asked for public comment.

The economists, who call themselves the Shadow Open Market Committee, warned the Fed that it may have tightened monetary policy too much and, if it has, may trigger a recession that is far worse than needed to slow inflation.

The group, headed by Carnegie-Mellon University Professor Allan H. Meltzer and Rochester University Professor Karl Brunner, said the "Risks of serious recession are increased by the absence of reliable information about the nation's money supply."

In Washington, Federal Reserve Board Chairman G. William Miller said today that inflation remains his agency's top concern and that it will continue to use monetary restraint to try to fight rising prices.

Although economists are divided over just how important the growth of the money supply is to inflation and output, nearly all agree now that inflation cannot be controlled when the money supply is growing sharply and that the economy's output cannot continue to grow when the money supply is expanding too slowly or is shrinking.

The Shadow Open Market Committee long has recommended that the Fed's Open Market Committee, which sets monetary policy, gradually reducc the rate at which the money supply is permitted to grow. It argues that the central bank usually lets the money supply grow too fast, permitting inflation to get worse than it otherwise would have been, then turns around and slams on the brakes, causing bad recessions.

The recent resurgence in short-term interest rates -- yields on Treasury bill rates at today's regular auction rose sharply -- suggests that the Feb plans to continue to let interest rates rise in order to hold down borrowing by corporations.

None of the other major banks that trimmed the prime interest rate to 11 1/2 percent a month ago followed the First Chicago increase today.

Citibank, New York's largest, traditionally changes its prime rate on Friday, using a formula that relates the prime to other short-term rates.

Chase Manhattan said today that it is "assessing" market conditions and "at this moment" has no "immediate plans to change the rate."

Although the prime rate is a good indicator of the direction of other short-term interest rates, it is less important to the overall banking picture than it was 10 or 20 years ago.