Both the money supply and business loan demand continued to grow rapidly this week, according to figures released today by the Federal Reserve, prompting speculation that the central bank will take steps soon to raise interest rates in order to slow money growth and the economy.

Late this afternoon, actions by the Fed suggested to analysts that the central bank wants to boost key interest rates to about 10 3/8 percent from 10 1/4 percent.

The Fed got out its clamps for the first time in months last Friday and Monday, boosting interest rates from 10 percent (about where they had been from early November) to 10 1/4 percent

If the bank continues its actions in the money markets, it may soon have to take the more dramatic step of raising the discount rate charged member banks to borrow from it. The rate is 9.5 percent.

Because the rate is so much lower than the open market rates, banks are stepping up their borrowing from the Fed to take advantage of the differential. Bank borrowing from the Fed rose $1.05 billion in the week ended May 2, from $851 million the week before.

In a related development, Chase Manhattan Bank announced this morning that it would raise the prime rate to 11 3/4 percent from 11 1/2 percent. That leaves only New York's Citibank, which just recently became the nation's largest, alone among major banks with a prime rate of 11 1/2 percent.

Many observers expect Citibank will raise its prime rate - the interest it charges its best corporate borrowers for a short-term-loan - Friday, when it makes its regular recalculation based on market interest rates.

In raising its prime rate, Chase said the rate is a "reflection of the cost of fund. In response to recent money market pressures, a quarter-point increase is appropriate at this time."

The Fed said today that the money supply - currency in circulation and checking accounts - grew $500 million in the week ended April 25, following a sharp $4.1 billion jump the week before.

For the past four weeks, the narrow money supply has been growing at a seasonally adjusted annual rate of 14.1 percent, far exceeding the central bank's target of 4 to 8 percent.

Still, despite the recent sharp increases in money growth, the money supply has been growing very slowly for the first three months of the year. When looked at over the past three months, the money supply is growing at a rate of only 3.1 percent.

Fed officials cautioned earlier this week that the sudden tightening in monetary policy - which came after Fed Chairman G. William Miller had publicly resisted pressure from the administration to do just that - did not represent a real tightening at all.

Officials said the steps were taken to assuage foreign and domestic money markets and convince money traders that the Feds would not let the money supply explode. Federal Reserve sources said they do not think money growth will be excessive (which nearly all economists agree leads to worsened inflation) and said the centrala bank is convinced that the economy is slowing doww nicely under current policy.

Government sources said the Fed's open market steps today - announcing a sale of government securities to drain banking system reserves at interest rates higher than in similar transactions last week - should not necessarily be interpreted as further tightening.

But analysts differed with the central bank. "There's no indication that money growth will slow over the next three months, although there may be a pause in late May or early June," according to Leon Gould, an economist with Commercial Credit Corp.

He said the Fed's announcement that it would make so-called matched sales at 10 3/6 percent suggests the central bank wants a federal funds rate (the interest banks charge each other for overnight loans and the Fed's key monetary polciy tool) of 10 3/8 percent, up from 10 1/4 percent.

Coupled with the continuing increase in business loan demand - New York city bank loans to businesses rose another $384 million in the week ended May 2 - the central bank will have to tighten up.

Analysts said the slow money and loan growth in the early part of the year reflect mainly big profit increases - which reduced corporate borrowing needs - and the effect of bad weather, which reduced business needs for loans to finance inventories.

Gould said he expects the federal funds rate to be up another quarter point by next week and perhaps a full point by the summer.