Top White House officials and congressional Republican leaders reached tentative agreement last night on a plan to satisfy President Reagan's demand for at least $4 billion in domestic appropriations cuts for fiscal 1982.

The plan would double the $2 billion in savings contained in a huge catch-all government funding bill vetoed by Reagan last month but would also partially shield major social programs from even deeper cuts sought by Reagan.

As a result, GOP leaders expressed strong confidence that Congress will approve the compromise and Reagan will sign it, ending a long stalemate over Reagan's proposed 1982 spending cuts and clearing the way for even bigger battles over the 1983 budget when Congress convenes in January.

A final go-ahead was withheld pending a decision by Reagan, which is expected today.

But, after the hour-long meeting last night, Office of Management and Budget Director David A. Stockman said of Reagan and the lawmakers: "He said he wanted to meet them halfway, and we will say this looks like it."

Almost as important was a tentative nod from Rep. Silvio O. Conte (Mass.), ranking Republican on the House Appropriations Committee, whose approval has been viewed as critical in winning support of moderate GOP "Gypsy Moths" in the House.

"I think we did pretty good," Conte said, claiming that fuel assistance for the poor and other social welfare programs fared relatively well.

With further consultations to win the support of conservative Democratic "Boll Weevils" in the House, "I'm very optimistic we can fly this thing," House Minority Leader Robert H. Michel (R-Ill.) said.

Although the House is controlled by the Democrats, whose leaders were not included in negotiations with the White House, Michel failed by only 12 votes to win House support last month for a similar although somewhat differently configured package of cuts. That means he would have to pick up only a few more Republican or conservative Democratic votes to win this time.

While the $4 billion in savings would meet Reagan's bottom-line demand for appropriations cuts, it leaves the president far short of the $16 billion in deficit reductions he urged last September atop $35 billion in budget reductions approved by Congress during the summer.

In addition to abandoning selective tax increases and cuts in benefit entitlement programs as being too controversial, Reagan had to meet Congress "halfway," as he put it, on the rest of the program by signaling he would accept $4 billion of the $8.4 billion in domestic appropriations cuts he originally proposed.

Congressional leaders, including Republicans, claimed they had met the $4 billion goal late last month when they cut roughly 2 percent off a huge "continuing resolution" to fund the government after earlier stopgap funding expired Nov. 20.

But the administration insisted that the savings amounted to no more than $2 billion. Reagan said that was not enough as he vetoed the measure in a dramatic confrontation with Congress that resulted in a one-day shutdown of most of the government until temporary funding was provided through Dec. 15.

Republican leaders said last night that they expect the new continuing resolution to be approved well in advance of the Dec. 15 deadline, thereby avoiding another crisis for the bureaucracy.

The new plan imposes a 4 percent cut on all domestic spending except benefit entitlements including food stamps, revenue sharing with states, veterans' health benefits, law enforcement activities and the judicial branch.

The cut also affects programs that already had sustained their full quota of Reagan-proposed reduction. This, in effect, means that programs already shielded by Congress would not have to bear the full brunt of the new cuts, which was important to Conte and others.

The new plan also drops an earlier Senate Republican proposal to give Reagan some discretion in allocating the cuts, an idea that drew fire from Democrats and some moderate Republicans who want Congress to have the final say over what is cut.

The troublesome issue of foreign aid remains unsettled pending the outcome of next week's House votes on the issue. One source said it was understood that foreign aid would be funded at the new House-proposed level or at the $10.1 billion figure included in the vetoed continuing resolution, whichever is lower.

This would mean substantially less for foreign aid than the administration wants, possibly necessitating a push for a supplementary appropriation.

While there was no firm decision on duration of the new spending authority, sources said GOP leaders are leaning toward extending it through the end of the fiscal year on Sept. 30, 1982, for any programs for which appropriations bills are not passed in the meantime.

Stopgap funding was needed in the first place because Congress had approved appropriations only for itself when the current fiscal year started Oct. 1. Such funding still is needed because only three other appropriations bills have been given final approval.

The Republican strategy has been to devise a compromise that can pass both houses in identical form, avoiding a House-Senate conference such as that last month when the previous bill was plagued by massive confusion about numbers that contributed to the veto confrontation.

An important part of last night's agreement was a consensus on a common numbers base for computing savings, which the Republicans considered crucial to avoiding another fight with the White House.

Stockman was joined in last night's meeting by White House Chief of Staff James A. Baker III, Reagan's congressional liaison chief Max L. Friedersdorf and Baker assistant Richard G. Darman. The session followed three days of intensive negotiations prompted by congressional GOP leaders' determination to avoid repetition of last month's confrontation.