House budget negotiators yesterday offered to make an additional $24 billion in domestic spending cuts over the next three years in a bid to break the House-Senate impasse that is threatening enactment of major deficit reductions.

Although a formal response from Senate conferees was delayed until today, the initial reaction from the Senate was skeptical.

"I am not that much more encouraged," said Senate Budget Committee Chairman Pete V. Domenici (R-N.M.).

"It looks more than enough to laugh at and less than enough to make you feel good," said Sen. Lawton Chiles (Fla.), the ranking Democrat on the Senate Budget Committee.

The House offer was designed to counter Senate criticisms that some House-proposed cuts were phony and to satisfy Senate demands that the House come up with savings to offset the money that would have been saved by freezing Social Security benefits and other government pensions, an estimated $28 billion over three years.

The benefits freeze, proposed by the Senate and opposed by the House, was abandoned in an accord with the White House last week that left senators fuming over what Majority Leader Robert J. Dole (R-Kan.) described as "surrendering to the deficit."

In outlining the House proposal, House Budget Committee Chairman William H. Gray III (D-Pa.) said the House was meeting four specific demands of the Senate.

He said the House was abandoning the savings it had claimed from revision of government contracting practices, moving closer to the Senate's defense spending figure, toughening enforcement provisions and satisfying Domenici's demand that three-year savings amount to roughly $270 billion.

Deficit reductions under the new House offer would amount to $272.6 billion over three years, starting with $56.9 billion next year. The proposal would come within range of halving deficits by fiscal 1988. The House plan projected the deficit for that year at $116.8 billion.

If the Senate has problems with the House proposals, it will be up to the Senate to offer alternatives, Gray said.

"If they are going to have a mov- ing target," he added, "we'll have a permanent impasse." Several House conferees described the offer as "close" to a bottom-line figure for the House.

But senators complained that some of the new cost-cutting measures proposed by the House are not likely to be approved, among them user fees on electric utilities that generate nuclear power and imposition of grazing fees for federal lands.

Some also claimed that cutbacks, such as an end to state royalties for mineral leasing, were aimed at western states represented by Senate budget leaders such as Domenici.

Domenici and other senators also claimed that the House was failing to live up to its agreement with the White House on the size of the defense budget. The House offered $298 billion in defense spending authority for fiscal 1986, about $4 billion short of what would be needed to keep pace with inflation, which was the agreement reached last week.

House members contend their deal with the White House was only to move toward a full inflation adjustment of $302.5 billion.

New cutbacks proposed by the House covered a variety of programs except for those oriented toward the poor, which conferees from both sides had agreed to protect.

Among programs the House would cut were farm supports, rural housing, Amtrak and mass transit, public housing, Medicare, a variety of economic aid programs, the Strategic Petroleum Reserve and Export-Import Bank direct loans.

The House also picked up savings assumed by the Senate from attrition in the federal work force and a 10 percent reduction in administrative costs of the government.

It would terminate eight programs, seven more than it originally proposed, most of them small and relatively inexpensive.

Even though the House offer was not expected to be accepted as a whole by the Senate, the key question appeared to be whether it was enough to get the talks going again after a nearly three-week impasse.