Americans continued to cut back sharply on their installment buying in June, the government reported yesterday, indicating that consumers still are striving to pay off existing debt and show no signs of taking on new burdens.

New figures published by the Federal Reserve Board show the total amount of installment credit outstanding in the United States plunged a record $3.46 billion over the month, more than matching the huge $3.43 billion drip recorded in May.

The new statistics came as the Chase Manhattan Bank abandoned an attempt to hold its prime lending rate to 10 3/4 percent and joined the rest of the industry in charging an 11 percent rate to its preferred corporate customers.

Chase had slashed its prime on July 24 but was unable to get others in the industry to go along. With borrowing costs to banks now on the rise again, some analysts believe the recent sharp drop in the prime has come to an end.

Meanwhile, several of the nation's leading retail chains reported a slight sales pickup in July, but the increase was small and not consistent throughout the economy. Spokesmen said consumers still appeared to be cautious.

The June figures on consumer credit showed a continuation of the trend that began earlier this spring: Americans are sharply paring the amount of new installment buying they're doing, while steadily repaying outstanding debt. n

The continuation of this earlier caution bolsters predictions by economists that consumers are unlikely to begin spending freely again very soon. As a result, hopes for a vigorous bounce-back from the recession still are dim.

The Fed said the total of new credit extended shrank to 14.7 percent of disposable personal income during the April-June quarter, compared with 18.5 percent the previous period and 20.2 percent in the second quarter of 1979.

At the same time, the amount of previous debt that consumers paid off remained relatively unchanged -- totaling 19.7 percent of disposable personal income last quarter, compared with 17 percent to 18 percent in the four previous periods.

New credit extended in June shrank to $20.7 billion -- down from $21.24 billion the previous month -- while the amount of old debt liquidated stayed at $24.16 billion, about the same as the $24.67 billion recorded in May.

The June decline in total outstanding consumer debt amounted to an annual rate of 13.5 percent, compared with a 13 percent pace the previous month and an 8 percent annual rate recorded in April.

By contrast, consumer credit grew by a booming 13 percent during 1979 and by a stunning 19 percent the previous year.

Analysts said the falloff this year stemmed from a variety of factors -- the decline in real income resulting from the past year's inflation, the sag in auto sales, and the credit restraints the Fed imposed on March 14.

The Fed's formal controls now have all been removed -- the monetary authority began phasing them out in mid-June and dismantled the last of them a few weeks ago -- but consumers so far have not rushed to take on new debt burdens again.

Within the overall totals, yesterday's report showed these trends:

The amount of new credit extended for automobile purchases fell $422 million, or 8.1 percent, in June. Total credit outstanding for auto loans fell $1.74 billion over the month, following a $1.34 billion decline in May.

New purchases involving credit cards -- at retailers, gasoline stations and banks -- plunged $454 million, or 4.5 percent, in June. At the same time, total outstanding credit card debt fell $748 million, after declining by $488 million in May.

However, new credit extended for a broad category of other miscellaneous loans actually rose during June by $195 million, although here, too, total credit outstanding fell $1.07 billion.

And new loans for mobile homes also edged up, rising $140 million over the month. The total amount of mobile home loans outstanding rose by $97 million in June, offsetting a $33 million decline the previous month.

Overall consumer credit outstanding in June totaled $301.0 billion, up 3.3 percent from a year ago.