House Democrats this week begin their first serious effort to decide how to reduce the federal budget deficit, and the chairman of the House Budget Committee says the key to success is in sharply slowing the growth of Pentagon spending.

Rep. William H. Gray III (D-Pa.), House Budget Committee chairman for only a few months, called the $55 billion deficit-reduction package approved last week by the Senate Budget Committee "a rebuke" to President Reagan by his own party and a challenge to get serious about cutting the deficit.

He said rejection of the administration's military spending priorities by the Republican majority on the Senate committee was significant. The Defense Department represents the "greatest built-in growth" in government spending, he said.

Stressing that he favors across-the-board equity in a budget package, Gray said there is growing support among his House colleagues for a genuine freeze on Pentagon spending next year, though he said various members interpret "freeze" differently.

Gray also criticized parts of the Senate committee's budget, saying it "hurts the poor." He predicted that many of the proposed cuts in domestic programs would be rejected by the House.

In an interview shortly after the Senate panel approved its budget, Gray said he refuses to be drawn into a bidding war with the White House, Senate Republicans or the financial community over the size of next year's budget cuts.

Dismissing as "a mistake" attention to a target of $50 billion in cuts in fiscal 1986, the Philadelphian said, "I am not focusing on a number. It's not the number that's important. What is important is what is your deficit in 1987 and 1988."

Gray, the first black chairman of the influential budget panel, said a substantial deficit-reduction package -- one that brings the deficit to about $100 billion in 1988 -- could be achieved with first-year cuts ranging from "the high $30s billions to the $60s," depending on the mix of policies.

His comments came as House Democrats prepared to examine options prepared by Gray's committee staff. Known as the "hard choices exercises," the process that begins this week is designed to educate House Democrats on the size of the problem they face in reducing the deficit and to help produce a consensus for specific approaches.

At this point, the only option not clearly listed in the questionnaire going to each House Democrat is higher taxes, left out on orders from House Speaker Thomas P. (Tip) O'Neill Jr. (D-Mass.). O'Neill reportedly told other Democratic leaders he did not want such an option included even in this preliminary exercise because he did not want to give Republicans a chance to claim that the Democrats again want to raise taxes to reduce the deficit.

But House Democrats will be able to propose tax increases in an open-ended question on the form, according to several persons familiar with the contents.

Gray spent much of the 90-minute interview discussing military spending.

The Republican-backed package approved by the Senate committee calls for the Defense Department budget to grow only with inflation next year, followed by increases of 3 percent above inflation in 1987 and 1988. Reagan had asked for the Pentagon budget to grow by roughly 6 percent after inflation in fiscal 1986.

"They reduced spending in the area of the greatest built-in growth, the Pentagon," Gray said of the Senate action.

In explaining the feelings of his Democratic colleagues, Gray noted that there are various ways to "freeze" the Pentagon budget. He spoke most approvingly of a freeze in budget authority, rather than in actual 1986 outlays, which he said would be an enforcement problem.

A freeze in budget authority would save $25.2 billion in fiscal 1986 and $63.2 billion in fiscal 1988, he said.

In contrast, the Senate committee action would save $19.2 billion in 1986 and $51.2 billion in 1988.

"You have just gone up $12 billion over where the Senate is," Gray said.

But he stressed that this would not represent any reduction in funds for the military, saying that under a freeze in budget authoriity, Pentagon outlays would rise $17 billion over their 1985 level.

Gray said that many House Democrats feel that if there must be a freeze on domestic programs, "a one-year freeze in Pentagon spending would not be detrimental to the nation's security."

"There is one point I want you to understand," Gray said. "Under every one of the defense options that will be presented to House Democrats , none of them has cut military spending in 1986 below the 1985 level. That's very important."

During the interview, Gray, munching on a cheese steak sandwich at the long conference table in the committee offices, reviewed a report his staff had prepared on the Senate Budget Committee package.

He predicted that Democrats will not go along with cuts in education, child nutrition and other programs for the poor that the Senate committee approved. He also singled out military pensions as an area of potentially greater savings.

On the controversial question of freezing cost-of-living increases for Social Security recipients, Gray refused to be pinned down about possible House action. He said, however, that in light of the freeze approved by the Senate committee, he is disturbed that the Republican-backed package would raise Medicare costs for the elderly.

"You're asking our elderly to bear a double burden," he said.

House Democratic officials said last week that Gray is under pressure from liberals to restore some of the cuts in social spending approved during Reagan's first term. They indicated that he had been lobbying them to scale back their demands, arguing that while he had supported their efforts in past years, conditions now merit greater, across-the-board sacrifices.

But these House sources said Gray thinks that he could not ask liberal Democrats to freeze or even cut certain domestic programs unless conservative Democrats support a freeze in Pentagon spending.

Rep. James R. Jones (D-Okla.), Gray's predecessor as chairman, said late last week that the Senate committee version offered the "framework" for a House budget. "The 'freeze-plus' option is the best possibility of a serious deficit-reduction package," he said.

Another leading House Democrat agreed that something more than a straight freeze has to be put together to produce sizable 1988 deficit reductions.

Gray praised the Senate committee for providing the "appearance of movement" on solving the deficit problem. But he said he wants to wait to see how Senate Majority Leader Robert J. Dole (R-Kan.) and Reagan respond before making a final analysis. "This is the completion of the first lap of what obviously is going to be a multi-lap race," he said.