Demand for U.S. home loans rose last week as a decline in 30-year fixed mortgage rates to a three-week low boosted applications for refinancing, the Mortgage Bankers Association said on Wednesday.

Average 30-year mortgage rates fell 0.19 percentage point to 5.17 percent in the week ended July 31, the lowest since 5.05 percent in the July 10 week.

The drop in borrowing costs pushed refinance applications up 7.2 percent to 1,996.7 last week, lifting total loan requests by 4.4 percent to 517.3, based on the industry group's seasonally adjusted indexes.

Although the refi gauge has jumped 35 percent from its June low, it remains well below the 6,000 level that it had topped for five weeks around the time 30-year mortgage rates sank to a record low of 4.61 percent in March.

Purchase loan requests, which have been stuck in a narrow range for months, rose just 0.9 percent last week to 264.4.

Despite a handful of surprisingly upbeat sales and price reports indicating a bottom, a swift rebound in the worst housing market since the Great Depression is not on the horizon, industry analysts agree.

Most folks are hopeful, based on all the numbers we've been seeing, that we've got a floor here and we're going to start seeing a long, slow recovery, said Jonathan Corr, chief strategy officer at Pleasanton, California-based mortgage software provider Ellie Mae.

We can't march around in victory yet, but we're starting to see the light at the end of the tunnel, he added.

A break from persistently gloomy housing news, including record foreclosures and a toppling in average home prices by more than 32 percent in three years, has emerged in the past few weeks from government and industry measures.

Pending home sales rose more than expected in June, for the first five-month string of increases in six years, the National Association of Realtors said on Tuesday.

Sales of both new and existing homes gained in June for the third straight month, fired up by relatively low mortgage rates and prices, as well as first-time-buyer tax credits.

House prices increased in May for the first time in three years, and the annual pace of decline slowed for the fourth straight month, Standard & Poor's/Case-Shiller indexes showed.

Just as souring sentiment helped crush the market, so will improved confidence help to rebuild housing, economists said.

You've got to continue to see some healing in the economy, Corr said. I don't think anyone will tell you that we're going to see a lot of appreciation over the next couple of years in housing.

Still to be seen is how high the U.S. unemployment rate will rise, a big factor in determining how much further the record pool of foreclosure properties grows.

Unemployment that is at a nearly 26-year high and headed toward 10 percent is keeping many prospective buyers out of the market.

For a related chart of mortgage rates, right click on the code: and select Related Graph.

(Editing by Leslie Adler)