Federal Reserve Board Chairman Paul A. Volcker yesterday gave a powerful boost to the Senate Republican drive for at least $50 billion in deficit reductions next year, predicting that, if successful, it could lead to lower interest rates.

He said $50 billion in deficit cuts is a "minimum threshold" to assure lower interest rates but emphasized that it must be accompanied by "follow-through" measures to keep deficits on a decline in future years.

Volcker's comments were made after a breakfast meeting with Senate Republican leaders, who are trying to put together a plan to cut annual budget deficits of more than $200 billion by half over the next three years, starting with $50 billion in spending cuts in fiscal 1986.

The GOP lawmakers took on the job after the White House, hampered by its reluctance to make big cuts in defense spending or to tamper with Social Security, failed to come up with sufficient spending cuts to meet its own target of deficits under $100 billion by fiscal 1988.

The Senate Republicans are considering an across-the-board spending freeze, including defense and Social Security, along with a long list of White House proposals for specific program cuts. They hope to have a draft of their plan by Feb. 1, a few days before President Reagan's budget request is scheduled for submission to Congress.

Although consistent with his earlier positions, Volcker's comments yesterday were significant in underscoring Senate Republican leaders' arguments that spending cuts, however painful, hold out the prospect of political reward through lower interest costs and a sustained economic recovery.

Senate Majority Leader Robert J. Dole (R-Kan.) interpreted Volcker's assessment as indicating that $50 billion in savings is "marginal . . . hardly enough" and suggested that Congress should aim for deficits even lower than the current goal of $100 billion by fiscal 1988.

Volcker declined to say how much interest rates would fall if Congress makes what he called "convincing" deficit reductions but emphasized that they would be "lower than they would otherwise be."

Stressing the correlation he sees between budget deficits and interest rates, he said, "The more you do the better. I don't think there's much chance of the Congress overdoing what is necessary."

Added Volcker: "I think if you're going to have a convincing program, you've got to begin starting in the area of $50 billion or higher in terms of immediate first steps, with some follow-through."

Volcker's appearance was the first of a morning-long series of meetings that included Treasury Secretary Donald T. Regan and White House chief of staff James A. Baker III, who will be swapping jobs in the second Reagan administration, as well as leaders of the Business Roundtable, an influential organization of top corporate executives.

Business Roundtable officials said after their meeting with the Republican leaders that their group has hired a public relations firm to help marshal support among employes, customers and suppliers to bring pressure on members of Congress for deficit reductions.

While refusing to endorse specific spending cut proposals, Volcker leaned heavily toward those that would guarantee savings in the long run as well as the short run.

This prompted suggestions from Assistant Majority Leader Alan K. Simpson (R-Wyo.) and Senate Finance Committee Chairman Bob Packwood (R-Ore.) that the senators explore a three-year modification of the formula for Social Security cost-of-living increases as well as an earlier proposal for a one-year freeze in benefits.

"I'm willing to look in almost any direction . . . to get us there," Packwood said.

But Dole indicated little enthusiasm for the idea, saying any tampering with the inflation indexing formula for benefits might trigger pressure for curtailment of tax-rate indexing, which he described as a "no-no."

"We're talking about what we've been talking about; nothing's changed," Dole said.

Later Packwood said his only real interest is in nailing down sufficient savings over three years, noting that denial of cost-of-living increases for one year also would accomplish that purpose because the base from which future increases are calculated would be lower.

Asked whether he would favor tax increases to reduce deficits if Congress cannot meet its targets through spending cuts, Volcker reiterated that he prefers to see the emphasis put on spending cuts but added, "If you can't do it on the spending side, then look elsewhere."

Packwood said he was "not sure" Congress can reach the target through spending cuts alone but refused to speculate about a tax increase. "I don't even want to cross that bridge because, the moment you do, people start slipping off the spending-cut bandwagon," the Finance Committee chairman said.

Also yesterday, leaders of several business organizations told Reagan at a White House meeting that a slowdown in the defense budget buildup and a delay in Social Security cost-of-living increases had to be part of any deficit reduction effort. The president was told that a slowdown in spending must "apply across the board, including defense," Alexander B. Trowbridge, president of the National Association of Manufacturers, said after the meeting.

He added that the group, which included the American Business Conference, the Business Roundtable and the U.S. Chamber of Commerce, also urged Reagan to consider a limit on inflation adjustments in Social Security and other programs.

Arthur Levitt Jr., chairman of the American Stock Exchange, said afterward that on Social Security, the president replied that his campaign promise not to tamper with the retirement system "made it very difficult to address that issue."

Levitt quoted Office of Management and Budget Director David A. Stockman as telling the group that "additional reductions" in defense "were going to be considered as part of the overall package."