The government's index of leading economic indicators plunged a record 4.8 percent in April, setting off new fears about how severe the recession will be.

The index is supposed to foretell economic trends for several months.

The April drop, which followed a 2.1 percent decline in March, was the largest since the Commerce Department began compiling the index in 1948. The biggest previous decline was 3 percent in September 1974, during the last recession.

Though the index is not infallible as to how deep or long a recession will be, the April figure immediately became part of this year's political debate.

Republican presidential candidate Ronald Reagan, campaigning at a rally in downtown Cleveland, cited the new figures as "shocking" and charged that President Carter's economic policies are "engulfing the country in lost jobs."

Campaigning in San Francisco, Sen. Edward M. Kennedy (D-Mass.) said the decline in the indicators is evidence that the nation is "sinking into the worst recession since the Great Depression" and blamed it on failed presidential leadership.

The White house issued a statement saying the president is concerned about the figures but is confident that declining interest rates would help "moderate the recession and lead to recovery."

Meanwhile, in another bit of bad news for consumers, the Agriculture Department reported that farm prices leaped to 0.9 percent last month, ending three months of declines that had helped hold supermarket prices down.

Separately, a number of big banks, including the Bank of America, the nation's largest, followed other major lenders in reducing their prime interest rate to 14 percent, from 14 1/2 percent.

The latest round of rate-cuting began on Tuesday. The prime, the interest banks charge their most creditworthy corporate customers, has been falling steadily in recent weeks in response to the weakening economy.

For seven months in a row the index of leading indicators has either fallen or remained unchanged. April was the first month in the current slide that all 10 components of the index have posted declines.

Courtenay M. Slater, the Commerce Department's chief economist, conceded that the drop in the index "signals a steep decline" in this April-June quarter in both overall economic output and industrial production.

However, Slater cautioned that, despite the size of the drop, the index "tells us little about the more distant future." She said the figure has "not proved to be a successful predictor" of the overall economic situation.

Economists now are predicting that the "real" gross national product -- the value of goods and services the nation produces, adjusted for inflation -- will plunge at a 7 to 8 percent annual rate this quarter, the worst since 1974.

In addition, the unemployment rate, which shot up to 7 percent in April from 6.2 percent, is expected to continue rising sharply. Some analysts believe it will reach 9 percent before starting to decline.

However, Slater reiterated the administration's view that the recent decline in interest rates and gradual ebbing of inflation would lay the groundwork "for the economic decline to level off and for recovery to begin."

President Carter told a political rally in Columbus, Ohio, on Thursday that because of the policies he has put into place "the tide is turning" on the economy and "we are building a brighter economic future."

Yesterday, Reagan parried that: 'The truth is today that the tide which he himself set in motion has become a tidal wave of more economic bad news." He said it was "resulting in lost jobs and more pain for our people."

The 0.9 percent rise in farm prices in May followed a plunge of 4.5 percent in April and a 1.7 percent decline in March. The increase stemmed primarily from higher prices for corn, broilers, potatoes, hay and oranges.

The decline in the leading indicators left the overall index at 126.3 percent of its 1967 average -- 9.9 percent below its level of a year ago. The index last rose in September 1979.

The largest single contribution to the April decline came from a sharp increase in the job layoffs. Other major factors were the contraction in the nation's money supply and the rise in raw materials prices.