President Reagan and Senate Republicans, at odds over how to reduce the deficit, agreed yesterday after meeting for almost two hours to form a small "working group" to begin negotiations aimed at ironing out their differences.

The goal of the new negotiations is to produce a single budget plan backed by the president and the Senate GOP leadership that could be taken to the floor, averting a contentious split between the White House and its Senate allies.

White House spokesman Larry Speakes quoted Reagan as telling a dozen leading Senate Republicans that "we share the same objective of a meaningful deficit-reduction plan without tax increases and without damaging our defenses or the solid economic recovery we are now experiencing."

In his nationally televised news conference Thursday night, Reagan appeared reluctant to compromise on the two major sticking points with Senate Republicans, Social Security cost-of-living adjustments (COLAs) and defense spending. The Senate Budget Committee has voted a one-year freeze on inflation adjustments and to sharply lower defense spending.

Yesterday, Reagan appeared to hint at flexibility on defense, urging the senators to identify which programs they would cut rather than only propose slower overall defense-spending growth. It is not clear, however, whether Reagan would agree to specific cuts once they are identified.

Speakes said Reagan also insisted that Pentagon spending not be "robbed" to pay for more domestic spending.

At the end of a 1-hour 50-minute luncheon yesterday in the White House family dining room, Senate Majority Leader Robert J. Dole (R-Kan.) suggested that the White House and senators return to the kind of negotiations that have been repeatedly used to settle differences between Reagan and Capitol Hill on the budget.

Reagan agreed to the idea, Speakes said. No members of the group nor a meeting time have been chosen, but it will be confined to White House officials and Senate Republicans, he added. Previous such negotiations have included House GOP members and Democrats.

Speakes said Reagan praised the efforts of Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) to hammer out a budget plan. "His budget plan differs from mine," the president acknowledged. "I know many of you disagree with mine and with his, so today I hope we can talk about what we can agree on and go on from there."

A White House official said the gap on defense spending is wide between Reagan and the senators. Reagan had proposed trimming $11.4 billion in spending authority next year, $8.7 billion in 1987 and $10 billion in 1988 from projections made last August. The Senate budget plan trims $31.2 billion, $48.6 billion and $74.8 billion, respectively, he said.

Speakes said some senators urged Reagan to compromise on defense and warned that he risks deeper cuts if he balks.

He quoted senators as putting "a great deal of emphasis" on moving quickly. But Speakes indicated that Reagan may eventually agree to compromise. "It's going to take some convincing of the president on these issues," he said.

The Republican senators attending the luncheon included Dole, Domenici, Jake Garn (Utah), Alan K. Simpson (Wyo.), Jesse Helms (N.C.), William V. Roth Jr. (Del.), Bob Packwood (Ore.), Paul Laxalt (Nev.), Mark O. Hatfield (Ore.), Barry Goldwater (Ariz.) and Frank H. Murkowski (Alaska). The White House officials included Secretary of State George P. Shultz, Defense Secretary Caspar W. Weinberger, Treasury Secretary James A. Baker III, national security affairs adviser Robert C. McFarlane, OMB Director David A. Stockman, legislative liaison Max Friedersdorf, communications director Patrick J. Buchanan and Speakes.