The Carter administration's latest attack on inflation will not bring home mortgage interest rates down from their record levels and may even force higher, housing and lending officials predicted yesterday.

Lending officials warned that the only thing that could bring mortgage costs down quickly is a severe recession. They said they believe that could happen.

But if the nation does not fall into a recession, home buyers can expect to pay 14, 15, 16 percent or more for mortgages for months to come.

"We don't see any major departure from the present with regard to mortgage rates or mortgage availability," said Kenneth Thygerson, chief economist for the U.S. League of Savings Associations.

Thygerson predicted mortgage costs will remain at or near record levels because the Carter plan does nothing to lower the cost of money for mortgages or to encourage people to save.

In the next few weeks, mortgage rates may move higher, because the cost of money for mortgages is still going up, Thygerson and other lenders predicted.

One of the Washington area's biggest mortgage lenders, Washington-Lee Savings and Loan, yesterday jumped its basic mortgage rate from 15.5 to 16.5 percent.

Washington-Lee President Richard Lawton said the increase was necessary because the only money the institution has to lend comes from the Federal Home Loan Mortgage Corp. and other secondary market sources.

The Home Loan Mortgage Corp. buys mortgages from savings and loans and resells them to investors. The interest rate on mortgage bought by the corporation at yesterday's weekly sale averaged 16.16 percent, up from 15.34 percent last week.

So long as interest rates on other loans are rising, mortgage costs will keep going up, explained Dale Riordan, chief economist for the Federal Home Loan Bank Board.

When short-term interest rates begin to come down, mortgage rates slacken, added James Christian, economist for the National Savings and Loan League. Right now, however, short-term rates are going up rather than down. The Federal Reserve is pushing rates upward to discourage business from borrowing.