Chase Manhattan Bank, the nation's third-largest, yesterday cut its prime lending rate from 20 1/2 percent to 20 percent amidst indications more reductions could follow soon.

The cut understood the continuing volatility of interest rates. Only last week the prime rate hit 20 1/2 percent, one percentage point below its record level last January. As recently as late April it was 17 percent.

Other short-term interest rates have been falling in recent days, including rates major banks have been paying for acquiring funds by issuing large certificates of deposit or by borrowing from other banks.

Both Treasury Secretary Donald T. Regan and Commerce Secretary Malcolm Baldrige predicted rates would fall in coming months. "I think we're on the high ground now," Regan told a group of businessmen. However, Regan said last week that he does not expect rates to drop below about the 15 percent level until perhaps next year.

Baldrige, meeting with reporters, expressed a similar view. The Commerce secretary said a sluggish economy this year could lead to a prime rate of 14 percent or 15 percent by year's end, but he added, "That's a hope, that's all." And even if rates fall now as expected, they "might even jiggle upward" again before reaching such levels in the final quarter, Baldridge said.

A leading Wall Street analyst, Henry Kaufman of Salomon Brothers, was less sanguine about the outlook for rates. He told a gathering of his firm's clients last night that he believes that both long-term and short-term rates will, "on balance," continue to trend upward while remaining highly volatile.

One factor helping keep rates high, according to analysts such as Kaufman, are fears of continued large federal budget deficits. Yesterday the White House conceded that even with additional spending cuts and a speedup in the sale of some assets, the fiscal 1981 deficit will be at least $5 billion higher than forecast in March.

White House spokesman Larry Speakes said David A. Stockman, director of the Office of Management and Budget, presented the Cabinet with a package of budget changes, including $500 million worth of budget recissions and spending deferrals and three-month postponement from july 1 of a proposed $420 million military pay raise.

"Overall, we are hopeful that these efforts will hold the budget deficit below $60 billion " Speakes said. In March, the deficit for the year ending Sept. 30 was estimated at $54.9 billion.

Meanwhile, the Commerce Department reported that the index of leading economic indicators rose 0.4 percent in April following an upward revised 1.8 percent in March. The revised March increase, which followed three consecutive monthly declines, is the largest one-month increase since September 1979.

The pattern of declines followed by increases in the index, which often foreshadows changes in the economy is consistent with predictions by a number of forecasters that economic activity is expanding little if at all this quarter but that the chances of a recession have dropped sharply.

Separately, the department also reported that the nation's merchandise trade deficit widened in April to $3.5 billion from $451 million in March. Part of the increase in the trade deficit stemmed from problems in the timing of when exports and imports were logged by U.S. Customs officials.

The April increase in the leading indicators was much smaller than that of March and might not be repeated for May. Of the 10 indicators available, eight rose, and the largest positive impact came from an increase in the money supply, which is going up much less swiftly this month than last. Moreover, the second-largest factor was an increase in sensitive materials prices which are calculated using a four-month moving average.