Housing and Urban Development Secretary Patricia Roberts Harris pledged support this week to the Carter program "to tighten government spending and bring down the federal deficit." But she told the annual convention of the National Association of Realtors, "We will not make arbitrary cuts or starve useful and needed programs."

Harris also insisted that there are no "cocktails" in existing HUD programs. She told a press conference that she is optimistic that "necessary HUD programs" would not be cut.

Harris said she plans to use her administrative power to hold the FHA morgage rate ceiling at 9 1/2 percent. That federal loan program for single-family home ownership enables buyers to get mortgages for nearly 1 percent below the conventional level. However, sellers now have to pay big premiums to lenders to meet the market for such long-terms investments.

In addition, Harris said there is no plan to raise the FHA ceiling of $60,000 on single-house loans nor to increase the payout period on mortgages from 30 to 40 years. She added that the relatively new graduated-payment mortgages, with low monthly payments during early years, are being used increasingly to enable borderline buyers become eligible for homeownership.

While conceding that private construction of rental housing is lagging, Harris refused to discuss whether a federal guarantee against future rent control might stimulate private apartment construction.

Harris told the realtors that "the most effective approach to moderating inflation in the housing field is that of curbing the general inflation in the economy."

Rep. William A. Steiger (R-Wis.), however, told the realtors that Carter's voluntary program for fighting inflation will not work. Steiger insisted that mandatory wage and price controls probably will have to be implemented within 12 to 18 months.

Harris did state that "voluntary price and wave restraints are not very effective" in controlling sharply increased costs of building materials, land development and home financing.

"We hope to launch a cooperative effort with state and local governments to mitigate the inflationary impact of local land use regulations," she said. "We have to move carefully in this area, however, in order to avoid jeopardizing planning activities designed to produce a healthier, more esthetic environment."