Senate Republican leaders moved to seize the initiative on budget deficits yesterday, introducing legislation to require more than $250 billion in spending cuts over the next three years.

Introduction of the measure as the first order of business for the newly convened 99th Congress came after what was described as a "sobering presentation" of deficit projections by Office of Management and Budget Director David A. Stockman to a caucus of all Republican senators.

Senators said Stockman indicated that deficits over the next three years will be $8 billion to $11 billion larger than the administration forecast only a few weeks ago, and that existing plans for spending cuts fall considerably short of the administration's goal of halving the deficit to less than $100 billion by 1988.

Counting so-called "off-budget" items that previously were not included in deficit calculations but will be included starting with next year's budget documents, the deficits would now be $225 billion in fiscal 1986, $240 billion in fiscal 1987 and $235 billion in fiscal 1988. Lawmakers said the higher figures are largely a result of the economic slowdown in the third quarter of last year.

This means that deficit reductions would have to be larger than proposed earlier -- for a total of roughly $266 billion over three years -- if the administration's target of a deficit of no more than 2 percent of the gross national product, less than half the current level, is to be met by 1988.

The 2 percent goal was embraced in the bill introduced yesterday by Senate Majority Leader Robert J. Dole (R-Kan.) and Budget Committee Chairman Pete V. Domenici (R-N.M.), who plan to use the legislation as a vehicle for specific spending cuts as they are nailed down over the next few weeks.

The bill contained no specific proposals, although Dole and Domenici are working on a spending "freeze" proposal that would include both defense and domestic programs and other lawmakers introduced separate freeze plans yesterday in both houses.

A freeze of some kind will be "the centerpiece of any reduction plan," Dole said.

A key component of such a freeze, the curtailment of cost-of-living increases for Social Security recipients, continued to pick up support as the No. 2 member of the Senate said he thought such cuts should be considered despite administration opposition.

"Somewhere along the line, I think the American people have to know that cost-of-living allowances . . . including Social Security . . . are going to have to be dealt with in a tough, gut-hard way," said Sen. Alan K. Simpson (R-Wyo).

"I think we look at everything . . . I don't believe we say it Social Security is off-limits to begin with," Dole said.

Instead of staking out a specific course of action, Dole appeared to be making a symbolic statement of intent aimed at putting Senate Republicans at the forefront of the deficit reduction effort, which he characterized as the most urgent business of the new Congress.

"We want to get out front," Dole told reporters after the Stockman briefing. "We want to tell the president not to pull us; we want to go."

Although this was in line with earlier Dole pronouncements on the deficits, his determination to pursue reductions appeared reinforced after the new projections from Stockman, which Dole characterized as "a little worse than I thought."

Senior Republicans plan to start meeting with White House officials immediately in an attempt to reach agreement on spending cuts, with an initial six-hour session scheduled for this afternoon and evening at Blair House. Dole said a "working group" will continue deliberations during the period before Congress gets down to real business after Reagan's inauguration Jan. 21.

None of the plans under discussion contemplates tax increases, which Reagan has ruled off-limits.

But several senators said after the meeting with Stockman that his projections, including an analysis showing that neither the administration's proposed spending cuts nor the freeze proposals meet the three-year targets, will increase pressure for revenue increases.

"There's no way you can get from here to there without taxes," said one Republican senator who contended that Congress, with or without administration backing, will have to raise taxes or admit defeat on deficits.

Dole has not ruled out tax increases but has said that spending cuts should be nailed down before other "options" are considered, a position he reiterated yesterday in comments to the Senate.

Senate Republicans' concern over budget deficits was echoed by House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.), who told the House that deficit reduction was the highest-priority item on his agenda for the year.

"These deficits will not take care of themselves," said O'Neill. "It is up to the president and to the Congress to take them on. No doubt the public will judge the success of this Congress by our willingness to make the tough decisions to get our fiscal house in order."

Among the deficit-cutting plans floating around Congress yesterday was one introduced in both houses by a bipartisan group of lawmakers that would freeze spending for next year at this year's level, achieving more savings than Reagan's spending-cut plan.

Also yesterday, Reagan told aides he found merit in a recent proposal by Stockman to combine the U.S. Bureau of Reclamation with the Army Corps of Engineers. The proposal has been resisted by Defense Secretary Caspar W. Weinberger and Interior Secretary William P. Clark.

White House officials said Reagan ordered them and Stockman to come up with a plan by next month to combine the two agencies' functions.