The Reagan administration and major housing industry trade groups said this week that they would support a bill to provide tax credits for up to half the interest that first-time home buyers must pay on their mortgages.

The measure has been introduced by Senate Finance Committee Chairman Robert J. Dole (R-Kan.) as a way of continuing to aid first-time buyers while cutting back on local governments' use of tax-exempt mortgage subsidy bonds. Such bonds have been criticized as costing the government far more than the benefits they provide.

The law, allowing issuance of tax-exempt mortgage subsidy bonds, is scheduled to expire at the end of the year. But the bond program has become enormously popular as high interest rates have made it more and more difficult to afford a home, and an overwhelming majority of both houses of Congress has signed on to repeal the "sunset" provision.

Dole and a small group of other senators, alarmed at the growing federal deficit and projections that show mortgage subsidy bonds costing the government more than $1 billion in lost revenue by 1988, have been casting about for a politically acceptable alternative.

Judging from the testimony at a Senate Finance Committee hearing Tuesday, they appear to have found one, although the endorsements were considerably less than enthusiastic.

Under the mortgage subsidy bond program, a local housing agency may issue tax-exempt bonds, which, because of the tax exemption, carry lower interest rates. The agency then uses the proceeds of the bond issue to finance below-market mortgage loans to first-time home buyers.

The money may be channeled to the home buyers through normal lending institutions such as savings and loans, or it may be allocated to builders to provide loans for specific subdivisions. Long lines of eager applicants have become common following announcements that such funds are available.

However, the program has come under attack from the Treasury, the Congressional Budget Office and the General Accounting Office as an extremely inefficient method of providing aid to home buyers. The GAO has calculated that the same level of assistance that cost the government $2.6 billion under the bond program could have been provided with tax credits at a cost of only $680 million, for "a savings of approximately $2 billion.

In addition, the Treasury contends that the "flood" of tax-exempt bonds issued under the program is damaging the market, driving up the cost of tax-exempt borrowing for other purposes. Assistant Treasury Secretary John E. Chapoton Tuesday reiterated the administration's desire to see the program expire.

However, Chapoton said, "If the program is continued over our objections, we support the approach of giving state and local governments the option of . . . distributing mortgage interest tax credits. . . ."

Under Dole's plan, a state would be able to exchange some or all of its bonding authority each year--each state is limited to a certain dollar volume annually--for authority to issue mortgage tax credit certificates. These certificates would entitle the home buyer to a tax credit of between 10 and 50 percent of his mortgage interest cost.

Local housing agencies would determine who would be eligible, just as they do for mortgage subsidy bonds, and hand out the certificates.

The home buyer would obtain a loan at the current market rate, make his payments and then use the certificate to obtain a tax credit for part of what he had paid. Dole said it is his understanding that the law allows for credits to be paid out in installments so the home buyer would not have to carry the higher payments all year before getting his tax benefit.

In addition, the credits would be refundable--a provision Treasury opposes--meaning that, if they exceeded the homeowner's tax liability, the difference would be refunded.

Representatives of the National Association of Home Builders, the National Association of Realtors, the U.S. League of Savings Institutions and the Mortgage Bankers Association of America all agreed that the program would be worth a try, although several of the groups had reservations or suggestions for changes.

Several were unhappy with a provision that would reduce a homeowner's interest deduction by the amount of his or her credit. In addition, fears were apparent that, if the credit program is a success, it could lead to abolition of mortgage subsidy bonds after all; most said they would like to see both programs in place, thus providing a maximum amount of flexibility to both the local government and the home buyer.