First National Bank of Chicago today boosted its prime lending rate from 11.5 to 11.75 percent, setting the stage for a new round of interest rate increases at the nation's major banks.

The move by First Chicago, the nation's ninth largest bank, reflects tightening by the Federal Reserve last Friday, as the nation's central bank moved to raise rates to fight inflation and help the sagging dollar on world money markets.

Last Friday the Fed boosted its discount rate -- the interest in charges member banks that borrow from it -- to a record 10 percent and raised its key open market interest rate target to 10.5 percent.

Analysts said it was hard to tell whether the Fed had raised that target again today. They said the central bank had troubles carrying out its open market operations because of a shortage of government securities in the hands of dealers.

The Fed carries out its open market operations by buying and selling government securities to keep its target -- the so-called federal funds rate -- within bounds set down by the policy-making Federal Open Market Committee.

The federal funds rate is the interest banks charge each other for overnight loans of excess reserves and that rate shot up close to 10 and 15/16 (fifteen sixteenths) percent in trading today.

Analysts said the central bank does not want the rate high, but that it was stymied in trying to lower the rate.

Because dealers and banks think the market is going to go down, they have not been holding government securities. As a result, according to Larry Shotwell of Commercial Credit Corp., there was a shortage of U.S. government securities for the Fed to buy today when it wanted to inject funds into the banking system.

That meant that the federal funds rate rose higher than the Fed wanted it to. "It should close up around 10 and 15/16 (fifteen sixteenths) percent or 11 percent and it should open pretty high tomorrow," Shotweel said.

"We're not sure what the Fed's target is," said one analyst. "It's at least 10.5 percent and it's no higher than 10 7/8. We think it's about 10 5/8 percent."

But whatever the Fed's actual target, it is clearly much higher than the 10 1/4 percent target that prevailed from Nov. 1 unitl last week, and the Fed's tightening will cause other major banks to fall in line behind First Chicago soon.

Since the rate of inflation in the United States has been Exceeding interest rates here, foreigners do not want to hold onto dollars. By raising interest rates, the Fed hopes to make it more attractive for foreigners to hold dollars.