The nation's major banks, spurred by new pressure from Washington to lower their interest rates, slashed their prime lending rates yesterday by an extraordinary 1 1/2 to 2 percentage points, the sharpest cut in recent memory.

The move began in mid-morning with Citibank, the nation's largest, paring its prime to 14 1/2 from 16 1/2 percent. The 14 1/2 percent prime quickly was adopted by Bank of American and Manufacturers Hanover Trust Company, the second- and fourth-ranked banks.

By late afternoon, a spate of other major banks had lowered their prime rates to 15 percent and 15 1/2 percent, and analysts were predicting the prime would plunge even further next week after the Memorial Day holiday.

The slide stemmed from two factors: First a continued falloff in loan demand in the face of the fast-worsening economy. And, second, new efforts by Washington to "jawbone" the banks into lowering interest rates.

On Thursday, the Federal Reserve Board announced that, in light of the heightened recession signs, it was cutting back sharply on the credit restraints that officials had imposed as part of President Carter's March 14 anti-inflation plan.

The White House issued a companion statement noting that, since the Fed's action would lower money costs for the banks, "the rates that banks charge their customers should also decline."

The statement continued: "We hope that banks will act promptly to pass on to their loan customers the benefits of the reduction in cost of funds they are now experiencing."

As if to confirm the falloff in loan activity, the Fed reported yesterday that the nation's basic money supply plunged $1.3 billion during the week ended May 14, partly offsetting a near-$6 billion explosion the previous week. e

The Fed also announced that commercial and industrial loans on the books of the nation's large banks fell $929 million during the period, following a slide of $1.37 billion the previous week.

The 14 1/2 percent prime marked the lowest that key rate has been since last October 9, three days after the Fed's initial round of credit-tightening. The prime peaked three weeks ago at a record 20 percent.

The prime is the interest fee that banks charge their most creditworthy large corporate customers. Although the prime does not directly influence consumer and mortgage rates, it does serve as the most visible symbol of interest rates.

Analysts pointed out that while the Fed's action on Thursday was dramatic, the easing of credit restraints was merely a recognition of what already had happened in the market and didn't break any new ground.

Alan Greenspan, former President Ford's chief economic adivser, said in a telephone interview the economy "is fading faster than we realize" and "credit demands are being pulled back at a fast pace."

Yesterday's announcement on the prime was greeted with a complaint by House Banking Committee Chairman Henry S. Reuss (D-Wis.) that many big banks actually have been lending to large corporate borrowers at rates well below their official prime.

Reuss said a survey by the Federal Reserve Board shows 66.96 percent of the business loans made by large New York banks so far this year have been at rates below the prime, compared to 28.8 percent in late 1979.

"The prime rate is supposed to represent what banks charge their biggest customers," Reuss asserted. He said discounting from that rate would "rip off smaller borrowers who are not going through the wringer . . . ."

A Fed spokesman said the survey to which Reuss referred actually was taken before the latest run-up in interest rates and actually may not show much of a disparity between the prime that banks posted and the rate they charged.

Bank analysts said larger banks have taken to discounting the prime in recent years to compete with foreign branches and commercial paper. Federal regulators haven't viewed the practice as untoward.

The $1.3 billion dip in the money supply, to a seasonally adjusted $370 billion, was in the basic measure known as M1-A. Using a broader calculation, know as M1-B, the money supply shrank $1.4 billion to $387.3 billion.

Meanwhile, the Fed disclosed separately that its policymaking Open Market Committee voted in a meeting May 6 to reduce the lower limit of its federal funds rate target to 10 1/2 percent from 13 percent.

The panel decided at an April 22 meeting to try to hold the federal funds rate to between 13 percent and 19 percent. The reduction May 6 was ordered after a telephone conference.

The panel also set the following targets for the money supply for the first half of 1980: M1-A, an annual rate of 4 1/2 percent; M1-B, an annual rate of 5 percent; M2, an annual rate of 6 3/4 percent.

The federal funds rate is the interest charged on overnight loans to banks.