NEW YORK — Mortgage rates for 30-year loans dropped to the lowest level on record amid signs the housing market may be set for a turnaround.

The average rate for a 30-year fixed loan fell to 3.91 percent in the week ended Thursday, the lowest in data dating to 1971, from 3.94 percent, Freddie Mac said in a statement. The average 15-year rate matched last week’s previous all-time low of 3.21 percent, according to the McLean, Va.-based mortgage-finance company.

The U.S. housing market, under pressure from tight lending standards and foreclosures that depress values, is showing signs of improvement. Purchases of previously owned homes rose to a 10-month high in November as the inventory of unsold properties shrank to the lowest level in six years, the National Association of Realtors reported Wednesday.

“Falling home prices meeting already low interest rates are driving affordability,” said Ellen Zentner, a senior U.S. economist at Nomura Securities International in New York. “Mix that with higher consumer confidence and job growth, and I can see why home sales appear to be lifting off the bottom.”

The U.S. property market still may fall further and not rebound until late 2012 or early 2013, when gains probably won’t match those seen before the housing boom ended in 2006, according to a survey of 109 economists released this week by Seattle-based Zillow Inc.