The nation's money supply soared by $7 billion in the week ending May 11, raising fears that interest rates could rise again if the Federal Reserve Board moves to dampen money growth.

Markets reacted immediately to the news yesterday, sending government securities sharply lower, while Treasury bill rates climbed.

At the same time, the Federal Reserve reported an upward revision in money growth in the previous week to $4.4 billion, making a rise of $11.4 billion in the narrow M1 measure of money in the first two weeks of this month. "It's an alarming development," one analyst said.

One reason for accelerating money growth could be the growing strength of the economic recovery. Yesterday a separate report showed widespread gains in orders for big-ticket factory goods in April. The Commerce Department reported that orders for durable goods rose by 2.4 percent over March to $81.85 billon, after seasonal adjustment.

The April level was close to that of January, when orders totalled $82.4 billion. The last month before that when orders topped $80 billion was in September 1981, the department said.

The April increase was the fifth in six months, and was somewhat larger than most leading analysts had expected. The report showed, however, that factory shipments were weaker than expected last month at $80 billion, up only one-half percent from March.

Aircraft orders, which were depressed in February and March, recovered, helping to push up orders for nondefense capital goods by 9.6 percent in the month. Defense orders--a volatile category--fell 3.8 percent in April from the March level, the Commerce report said. Auto orders were "fairly flat," a Commerce official said.

The main question mark over the recovery has been whether consumers will start to spend more and to buy enough to sustain rising output.

A survey of consumer attitudes released yesterday showed that consumers are now more optimistic about the economy than they have been for six years. The study, by the University of Michigan, said that the index of Consumer Sentiment rose to 89.1 in April from 80.8 in March. Fifty-one percent of families surveyed reported recent improvement in the economy, and 53 percent expected business conditions to improve in the coming year. The last was the highest percentage for a quarter of a century.

Many analysts fear that the economic recovery will be slower than previous postwar recoveries, in large part because interest rates are still unusually high in comparison with inflation. For a while last month, after the money figures improved, financial markets hoped that the Fed would ease monetary conditions further and encourage another rate decline.

The Fed no longer gears its monetary policy as closely to M1--which includes currency in circulation and all checking accounts at financial institutions--as it used to. Fed Chairman Paul Volcker has warned that banking changes such as the introduction of money market deposit accounts at banks have made the M1 figures very difficult to interpret.

Nevertheless, a sharp climb in the money numbers is likely to make the central bank hesitant about encouraging further declines in interest rates, and may lead it to tighten credit slightly, analysts say. M1 grew very rapidly in the first three months of this year, before declining in April.

However, the seasonal-adjustment factors for April are notoriously unreliable, and Federal Reserve Governor Nancy Teeters cautioned recently that the attempts to smooth out seasonal increases in money balances in April could upset the figures for the months on either side. It is likely that the seasonal adjustments artificially lowered April's money total, and now are contributing to May's increase.