Several of the nation's major banks announced further reductions in their prime lending rates yesterday as new figures showed a marked slowdown in the growth of consumer credit, partly in response to the recent credit-tightening.

In a round of rate reductions, Chase Manhattan Bank, the nation's third-largest, lowered its prime rate to 17 percent from 18 percent, while others pushed theirs down to 18 percent and 17 1/2 percent.

The actions came as the Federal Reserve Board reported that the growth in consumer credit across the nation slowed significantly during March, in part because of the government's March 14 anti-inflation program.

The Fed said the total amount of consumer installment debt outstanding rose by $1.43 billion in March, down from a $2.3 billion jump in February. The March increase was at a 5.5 percent annual rate compared with 9 percent for February.

More important, the figures show that new credit fell a hefty 1.6 percent over the month, while repayments of outstanding debt rose by a similar amount. The amount of auto loans outstanding plunged during March.

Oficials said the statistics don't fully reflect the impact of the Fed's most recent credit-tightening moves, which were announced March 14 as part of President Carter's new anti-inflation program.

Consumer credit is expected to be even weaker in April. Analysts report that many Americans apparently have interpreted the Fed's stance as a sign that installment buying is either illegal or unpatriotic, and have cut back sharply.

The reductions in the prime rate from a record 20 percent level only two weeks ago reflect a drop in the banks' cost of obtaining funds and a sharp falloff in loan demand in the-face of the current recession.

Key economic indicators have been falling so sharply in recent weeks that many economists are beginning to fear that the recession may prove as severe as the 1974-75 downturn, which was the sharpest in 37 years.

Alan Greenspan, former president Ford's chief economic adviser, has predicted that the nation's real economic output, adjusted for inflation, will decline during the current quarter at an annual rate approaching 7.7 percent.

The nation's unemployment rate, a visible indicator of the country's economic health, shot up to 7 percent last month from 6.2 percent the month before. The Carter administration is predicting a top rate of 7.2 percent.

The prime rate is the interest banks charge their most creditworthy corporate customers. It doesn't affect home mortgage and consumer loans directly but it does influence them indirectly.

The Fed has been allowing interest rates to fall in recent weeks, but has yet to dismantle its March 14 credit restraints. The agency lifted a 3-percentage-point surcharge on loans to large banks Tuesday, but this was considered a modest step.

The Fed's report on consumer credit showed revolving credit outstanding rose by $611 million in March compared with a $575 million increase the previous month, while loans for mobile homes edged up $128 million, following a $198 million rise.