A measure of the number of applications to buy a home or refinance an existing mortgage held last week at the highest level since early May, a private group’s survey found.

A reading of 724.8 in the Mortgage Bankers Association’s gauge of loan demand for the week ended October 1 compared with 724.7 the prior week. The last time the index was higher was in the first week of May.

The average rate on a 30-year fixed mortgage has held below 6% since early July.Refinancing,a source of cash for consumers that helped support the economy last year, increased for the fifth straight week, the longest stretch since February-March. The refinancing index was the highest since April.

“We’re seeing a stability in mortgage rates which is fueling demand for mortgages and refinancing,” said the president of Americana Mortgage Group Inc., Bob Moulton. Americana Mortgage is the no. 2 real estate broker on Long Island.

The mortgage bankers group’s refinancing index rose 2.7% last week to 2270.8 from 2211.1.The gauge of applications to purchase homes fell 2.2% to 459 from 469.1 the week before.

Applications to refinance made up 47.1% of total bids last week, up from 45.9% the week before. Low interest rates have kept refinancing strong. Over the past year, the rate on a 30-year fixed mortgage has averaged 5.81%; lower than the average 6.68% of the past five years,according to MBA statistics.

The average rate on a 30-year fixed mortgage increased to 5.78% last week from 5.64%, the first rise in a month, the bankers’ association said. Mortgage rates are tied to yields on longterm securities such as 10-year Treasury notes.

The yield on the 4.25% note due August 2014 fell below 4% early last week and on September 22. Since then, yields have increased on signs the economy is accelerating.

At the current mortgage rate, borrowing costs on a $100,000 loan would be $585.48 a month, up from $576.60 at the prior week’s average rate. When mortgage rates were a record low 4.99% in June 2003, monthly borrowing costs were $536.21.

The average rate on a 15-year fixed mortgage rose to 5.2% last week from 4.99%. The rate for a one-year adjustable rate mortgage rose to 3.97% from 3.92%.

The share of adjustable rate mortgages of all applications rose to 33.9% from 32.5%.

Low borrowing costs and stronger home sales helped boost August construction spending by 0.8%. The $1.02 trillion annual rate reported by the Commerce Department on October 1 was a record.

New home sales, measured at the time a contract is signed to purchase a home, jumped 9.4% in August, according to the latest government figures.

“We continue to see very strong demand,” KB Home Chief Operating Officer Jeffrey Metzger said last month. KB, based in Los Angeles, is seeing a deceleration in home prices for the most expensive markets in America, Mr. Metzger said.

Housing is an issue in this year’s presidential campaign, with President Bush saying his policies have contributed to record home ownership levels. Democratic challenger John Kerry said Mr. Bush hasn’t done enough to ensure that housing is available and affordable.

The National Association of Realtors and Fannie Mae expect sales to slow next year as interest rates rise and the pool of eligible buyers gets smaller. Sales of existing homes fell to a 6.54 million-unit annual rate in August, the National Association of Realtors said on September 24.