The head of the agency that regulates Fannie Mae and Freddie Mac said Tuesday that interest rates on U.S. mortgages have further to fall and that a reduction of up to 1 percentage point would be reasonable based on historical data.

"Certainly one would think another 50 basis points easily and maybe a hundred," James Lockhart, the director of the Federal Housing Finance Agency, said during an interview on CNBC. Mortgage-backed securities issued by Fannie and Freddie largely determine a mortgage's interest rate. "You could see [those] rates are significantly higher than Treasuries, so … they could come down."

In its most recent survey, Freddie Mac reported that rates on the benchmark 30-year fixed-rate mortgage set another record low, averaging 5.14% for the week that ended Dec. 24, down from 5.19% the previous week.

Answering a question on CNBC, Mr. Lockhart said the key to any near-term drop in mortgage rates will be the Federal Reserve banks' efforts to buy up to $600 billion in mortgage-backed debt from financial firms, and a similar program worth $50 billion from the Treasury Department.

As a result of those moves, "hopefully, naturally, we'll see those rates continue to fall," Mr. Lockhart said.

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