The average rate on the 30-year fixed mortgage rose this week for the first time this month, though it remained below 4 percent for the eighth straight week.

The low rates may be contributing to a slow turnaround in the depressed housing market. Still, many who can afford to buy or refinance a home have already done so.

Freddie Mac said Thursday the average rate on the 30-year fixed mortgage rose to 3.98 percent this week. That’s up from 3.88 percent the previous week, which was the lowest level on rec­ord.

The average on the 15-year fixed mortgage also rose to 3.24 percent, from 3.17 percent the previous week. The 15-year mortgage hit a record low of 3.16 percent two weeks ago.

Mortgage rates are low because they tend to track the yield on the 10-year Treasury note, which fell below 2 percent this week.

For the past three months, the 30-year fixed mortgage rate has hovered near 4 percent. Sales of previously occupied homes rose in December for a third straight month. Homebuilders are slightly more hopeful because more people are saying they might consider buying this year. And home construction picked up in the final quarter of last year.

Still, sales of new homes fell in December, the Commerce Department said Thursday. About 302,000 new homes were sold last year, making 2011 the worst year for new-home sales on records dating back to 1963.

High unemployment and scant wage gains have made it harder for many people to qualify for loans. Many don’t want to sink money into a home that they fear could lose value over the next few years.

Builders are hopeful that the low mortgage rates could boost sales next year. Low rates were cited as a key reason the National Association of Home Builders survey of builder sentiment rose strongly in December and January.

For the five-year adjustable loan, the average rate rose to 2.85 percent from 2.82 percent. The average on the one-year adjustable loan was unchanged at 2.74 percent.

The average fee on the five-year adjustable loan was unchanged at 0.7; the average on the one-year adjustable-rate loan was unchanged at 0.6.