Chairman Jake Garn (R-Utah) of the Senate Banking Committee and Chairman Mark Hatfield (R-Ore.) of the Senate Appropriations Committee yesterday endorsed a $5 billion program for subsidizing mortgage interest rates for buyers of new homes, despite the Reagan administration's opposition to the plan.

The five-year program, developed by the homebuilding industry, is being introduced by Sen. Richard Lugar (R-Ind.), chairman of the housing subcommittee, with 18 cosponsors.

The backing of Garn and Lugar, the two top Republicans in Congress on housing matters, is a significant victory in Congress for the idea.

It also is a repudiation of Reagan administration policy and pronouncements.

Administration officials said privately after the Lugar bill was announced that the White House could not go along with the idea because of its initial $1 billion budget impact. A Cabinet-level task force, chaired by Housing Secretary Samuel R. Pierce Jr., is looking at ways of stimulating the housing industry and must come up with a proposal by the end of this month.

The plans receiving the most favor involve low-cost tax incentives, administration sources have said.

Pierce told a lunch group in New York on Tuesday that the administration must avoid subsidizing interest rates, because the large cost of such a program could wreck the economy and lead to a depression like that in the 1930s, UPI reported.

But Congress already is moving in that direction without the administration, and the strong backing from congressional Republicans may push the White House toward acceptance of the idea.

Lugar and Garn both point out that the plan involves a payback of the subsidy by the homebuyer when the home is refinanced or sold. Lugar also has argued that the jobs created in the housing-related industries would stimulate the economy and produce enough tax revenues to pay for the plan.

Garn took pains in his endorsement statement to blame the current problems of the housing industry on "policies of previous administrations and Congresses."

"This is not another federal giveaway program or a federal bailout. It is a well-considered one-time boost for one of our country's most important industries," Garn said.

Under the proposal, up to 450,000 low- and moderate-income families would be able to buy homes at interest rates 4 percentage points below the FHA rate for five years, and then at the FHA rate for 25 years unless refinanced. At today's FHA rate of 15 1/2 percent, a government buydown to 11 1/2 percent would reduce monthly payments on a $65,000 mortgage from $848 to $644, Lugar said.