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By Sweta Singh

July 18 (Reuters) - The U.S. housing sector has seen prices, sales and financing applications soar lately as more buyers entered the market for the first time, but those trends were hard to see in big banks' mortgage businesses during the second quarter.

Four major U.S. lenders reported an average 33 percent drop in second-quarter mortgage banking revenue on Friday, compared with the same quarter of last year. An ongoing decline in refinancing activity, higher funding costs, tougher competition and a greater portion of business coming from third parties, who generally deliver lower margins, all contributed to the slide.

Even so, executives sounded optimistic about the core operation of lending to people who want to buy homes.

"I wouldn't throw in the towel on the mortgage business," Tim Sloan, chief executive officer of Wells Fargo & Co, the biggest U.S. home lender, said on Friday.

Wells's quarterly mortgage banking revenue of $1.4 billion was down 19 percent from the year-ago period. A variety of factors hurt results, including the sale of a legacy portfolio of risky loans, but Wells saw improved credit quality among borrowers, and strong demand for mortgages to purchase new homes. The bank sees "huge opportunities" in growing first and second mortgages, Sloan said.

JPMorgan Chase & Co, PNC Financial Services Group Inc and Citigroup Inc also reported mortgage banking revenue declines of 33 to 41 percent last week. Bank of America Corp reports results on Tuesday.

Starting in 2009, banks began to benefit from a surge in mortgage refinancing, thanks to rock-bottom interest rates and federal programs to help struggling borrowers. That activity has been trailing off as rates have started to rise and many borrowers who sought lower rates have already gotten fresh loans.

It will be difficult to make up for lost refinancing volumes, even though the market for home purchases has been improving, analysts said.

New and existing home sales rose in May while prices reached all-time highs, according to federal housing data and the National Association of Realtors (NAR). Weekly mortgage applications shot to a seven-year high at one point during the quarter, according to data from the Mortgage Bankers Association. NAR predicts new single-family home sales will rise 8.4 percent this year.

Those improvements in the market may continue for some time, analysts said, since mortgage rates remain low by historical standards and young American millennials have only recently begun to enter the housing market. But banks' mortgage businesses will only show improvements as comparisons with a previous year become easier, they said.

"While we saw some pressure in the second quarter, we think that's a low point for the year," Marty Mosby, an analyst at Vining Sparks brokerage and asset manager, told Reuters. "We should start to see some pickup in home purchase activity." (Reporting by Sweta Singh in Bengaluru; Additional reporting by Dan Freed and David Henry in New York; Editing by Lauren Tara LaCapra and Phil Berlowitz)