NEW YORK - U.S. mortgage rates held at their lowest level since late May in the latest week, low enough to continue to spur home loan demand and help the hard-hit U.S. housing market recover.

Attractive rates are a positive for the U.S. housing market, which has been showing some signs of stabilization, with sales rising and home price declines moderating in many regions of the country.

Interest rates on U.S. 30-year fixed-rate mortgages averaged 5.04 percent for the week ending September 24, unchanged from the previous week, according to a survey released on Thursday by home funding company Freddie Mac.

That is the lowest rate since 4.91 percent in the week ending May 28. Mortgage rates have hovered around 5 percent, widely viewed as a key psychologically level, for several weeks.

The mortgage rate, however, is still significantly higher than the record low of 4.78 percent set the week ending April 2. Freddie Mac started the Primary Mortgage Market Survey in 1971.

Michael Moskowitz, president of Equity Now, a direct lender based in New York City and licensed in 17 states, said when interest rates on mortgages jumped in June, refinancing activity at his company slowed down by at least half.

Thank goodness rates came back down now, he said.

Mortgage rates remained above 5 percent for a seventeenth straight week.

The level of interest rates on mortgages plays less of a role on purchase home loan demand than it does on refinancing activity, but demand for both rose last week.

The Mortgage Bankers Association said its seasonally adjusted index of mortgage applications, which includes both purchase and refinance loans, increased 12.8 percent in the latest week, the highest since the week ended May 22.

Other data on Thursday, though, confirmed the housing market was still weak.

The National Association of Realtors said sales of previously owned U.S. homes unexpectedly fell in August.

Thirty-year mortgage rates have been falling for most of this year after the Federal Reserve unveiled its plan to buy mortgage-backed debt in late November. The Fed from time to time met resistance in the bond market.

The U.S. government has acted to try to bring mortgage rates down to levels that would spur demand and help the battered housing market to begin to recover.

The central bank is aiming to keep interest rates on mortgages low for home buyers through early next year, extending its mortgage-backed securities purchase program to March 31, 2010, while keeping the size constant at $1.25 trillion.

Mortgage rates are linked to both Treasury and MBS yields.

The battered U.S. housing market, which has suffered the worst downturn since the Great Depression, is both the source and a major casualty of the credit crisis. A recovery of the market could hasten a turnaround for the United States, the world's largest economy.

(Additional Reporting by Lucia Mutikani; Editing by Padraic Cassidy)

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