The Reagan administration is now at work on an entirely new round of large and controversial budget cuts, which White House officials say must be made if the president's "economic recovery program" is to succeed.

The new reductions will be added to those envisioned in the budget resolution that the House of Representatives endorsed in a vote last Thursday that exhilarated the administration but did not solve its problems, these officials say.

In the weeks ahead the Reagan administration hopes to propose controversial new cuts in Social Security benefits, additional reductions of as much as $6 billion in government spending this year, and a new defense plan that may chop back the large spending increases previously endorsed. In addition, the White House probably will initiate a confrontation with the House and Senate Agriculture committee, which are currently writing four-year farm bills that far exceed the spending limits in the House and Senate budget resolutions.

The White House avoided these and other potentially contentious steps in recent weeks while it lobbied the House for its version of the budget resolution. "We don't want to do anything that can screw up this vote," a senior White House official, with direct responsibility for budget-making, said last week just before the House voted.

White House officials say they need the additional cuts for several purposes; to hedge against the real possibility that outlays will be higher than predicted because interest rates and unemployment remain high; to persuade edgy members of Congress and nervous financial markets that the economy can afford the tax cuts Reagan wants to make; and to improve the prospects for achieving a balanced budget by 1984, the most important political objective of the Reagan program.

The farm bill may be the first symbolic showdown.to avoid antagonizing members, the White House watched in silence as both committees authorized price supports for milk, wheat, cotton and other commodities that are much more expensive than the Reagan budget would permit. The committees warmed the hearts of the principal agricultural interest groups, but they set exactly the precedent the White House is most anxious to avoid.

If other authorizing and then appropriations committees were to follow that example as they deal with budget specifics this summer and fall, the budget resolution approved last week would be meaningless. According to senior officials, the administration is determined to make the budget resolution stick by fighting for its spending levels throughout the budget process.

Sources close to David A. Stockman, director of the Office of Management and Budget, predict jauntily that Congress will eventually make deeper cuts in domestic spending, including Social Security, than the administration has sought. But meanwhile, Stockman is looking for new cuts, probably in the form of deferred outlays now scheduled for the current fiscal year. According to sources in the White House, Stockman would like to find $5 billion to $6 billion of cuts in this category, although no hint has yet been given of where they might come from.

Another target Stockman has in mind is the defense budget, now scheduled to grow dramatically during the Reagan administration. White House officials acknowledge that the initial defense spending figures in the president's economic plans were largely guesstimates, although they accurately reflect the administration's determination to increase defense outlays vastly.

According to informed sources, Stockman is hoping that the administration will be able to use the announcement of its five-year defense plan as a vehicle for reducing somewhat its spending estimates without appearing to abandon its buildup. These sources said Stockman would not be displeased if political pressures grow for a somewhat more restrained defense program.

At the Pentagon, however, Defense Secretary Caspar W. Weinberger has said repeatedly that the administration will stick to the defense program it has already announced, and will actually spend more than announced if the rate of inflation proves higher than the administration's optimistic estimates.

As reported earlier, Stockman has also concluded that the White House must abandon its initial pledge not to cut back Social Security, where the administration is now seeking reductions of about $8 billion a year.

The administration is almost forced now to turn to defense and Social Security if it wants to reduce spending further. They together make up about half of the budget, and most of the feasible cuts in the other half have already been proposed.