The Reagan administration joined Senate Republican leaders yesterday in an extraordinarily harsh attack on the deficit-reduction plan adopted Thursday by the Democratic-controlled House Budget Committee.

In a letter to Senate Majority Leader Robert J. Dole (R-Kan.), Office of Management and Budget Director David A. Stockman said the plan "amounts to a fundamental retreat on defense and a total abdication of responsibility on the domestic spending side."

The House committee proposed to freeze defense spending at the current level of $293 billion next year, while the Senate, in a plan endorsed by President Reagan, would raise it to $302.5 billion to accommodate inflation. The House Budget Committee also cut domestic spending by about one-third less than the Senate did for next fiscal year, with a considerably wider gap in future years.

In a news conference, Dole and Senate Budget Committee Chairman Pete V. Domenici (R-N.M.) denounced the House committee's budget and released Stockman's letter analyzing it.

"I'm disappointed that my dear friends Pete Domenici and Bob Dole would put on such a display," said House Budget Committee Chairman William H. Gray III (D-Pa.). "I don't quite understand why they would react in such harsh tones and with such a lack of civility. They must be feeling terrific heat for the policy mistakes they made on Social Security and Pentagon spending . . . . Pete and Bob know better than to say what they did and I am disappointed in them," he said.

On Social Security, the Senate eliminated cost-of-living increases for retirement benefits for a year, while the House panel voted to pay the full inflation adjustment.

In a second day of heavy criticism of the House Democrats' plan, Dole said at his news conference with Domenici that it was a "blueprint for economic disaster," with "more funny money savings than real deficit cuts."

Stockman's analysis said at least $14 billion, or one-fourth of the $56 billion in fiscal 1986 deficit reductions claimed by the House panel, "come from gimmicks, not policy changes."

Among other points, Stockman questioned $3 billion in claimed defense outlay savings, $4 billion from an assumption of government contracting savings and $4 billion from settlement of a dispute over outer continental shelf litigation.

"Under the guise of honest budgeting, the House Budget Committee has offered up a cynical concoction of exaggerated savings, numbers gimmicks and political posturing that adds up to a total abdication of responsibility in the face of the nation's fiscal problems," said Stockman.

Brushing aside the "funny money" charges, Gray said, "I think what they may disagree with is our policy choices." In reference to the Republicans' claim that the House committee would "mutilate" the Pentagon budget, as Dole put it, Gray also questioned whether the Republicans know what they want for defense. He noted that Reagan has several times dropped his minimal demand for defense and added, "Who knows, by next week he may be below our figure."

Dole said he hoped House Republicans would move to bring the Democrats' budget more in line with the Senate version, but sources indicated that the Republicans have not set their strategy. One fear is said to be that, if a GOP effort failed badly, it would only strengthen the hand of the Democrats in bargaining over a final budget in conference with the Senate.