The nation's money supply plunged by $3.7 billion in the last week of June, the Federal Reserve reported yesterday, and analysts said this paves the way for further declines in interest rates next week.

Treasury bill rates fell swiftly after the announcement of the money supply figures. Three-month bills dipped below 11 1/2 percent at one point in late trading, down from 11.73 percent on Thursday and 12.78 percent at the beginning of this week. David Jones of Aubrey G. Lanston and Co said "on the heels of this welcome drop in money, there has been a dramatic drop in the federal funds rates to a 12 1/2-14 percent range from 14 1/2 to 15 percent as recently as a week ago."

Gold prices soared yesterday, and the dollar fell against major currencies as markets anticipated further falls in interest rates. High U.S. interest rates previously had pushed the dollar up sharply and had helped to depress gold. Yesterday gold climbed to $345 an ounce in New York from $322.6 on Thursday. The dollar slipped to 2.486 marks in New York from 2.5065 in Europe Thursday and declined against other currencies.

Yesterday's reported drop in the money supply means that the Federal Reserve has more leeway in its credit operations and can allow interest rates to fall without endangering its money supply targets. Money market dealers believe the Fed eased credit this week, and thus encouraged the sharp fall in interest rates.

In the latest three weeks, the key M1 measure of the money supply--which includes currency in circulation and all checking accounts--has dropped by $8.9 billion, so that it is now in the bottom half of the Fed's target range. Until yesterday's report, M1 had been growing above the top of the Federal Reserve's target range, making it hard for the central bank to ease credit conditions.

Analysts are expecting a big rise in the money supply to be reported next week, but there now appears to be plenty of room within the targets to absorb the predicted bulge.

M1 averaged a seasonally adjusted $445.9 billion in the week ended June 30, the Fed report said. The previous week's figure, orginally reported at $449.9 billion. was revised down by $300 million to $449.6 billion.

M2, a broader measure of money, which includes some money market funds and time deposits, rose to a seasonally adjusted $1.907 trillion in June from $1.898 trillion in May. The $9 billion rise was much smaller than the increases recorded in each of the previous three months.

Business loan demand at the nation's major banks rose by $3.39 billion in the week ending June 30, after a gain of only $14 million the previous week, the Federal Reserve Bank of New York reported yesterday.

Money supply figures are extremely volatile, and this year have puzzled the Fed and other analysts by showing stronger-than-expected growth despite the deep recession. The Fed decided earlier this year not to try all out to bring M1 back within its target range, given the weakness of the economy. Nevertheless, the above-target growth put pressure on the Fed to keep credit tight.

Treasury officials have blamed this year's persistent high interest rates on erratic money growth, and have complained that the Fed allowed the money supply to grow too rapidly in recent months. However, most experts believe that it is very difficult to control the money supply closely on a weekly or monthly basis, and that short-run fluctuations do not matter much anyway.

The evidence is now "pretty persuasive" that the Fed has eased money market conditions, Elliot Platt of Donaldson, Lufkin, Jenrette said yesterday. However, it is more likely that the easing is a technical reaction to slower money growth than that the Fed has changed policy, analysts said. Chairman Paul Volcker is due to testify before Congress this month on the Fed's tentative targets for next year's money growth and he is very unlikely to announce a change in this year's targets, a New York economist said yesterday.