Demand for U.S. mortgages bounced from seven-month lows last week as average 30-year borrowing costs were unchanged, helping ease pressure for aggressive Federal Reserve actions to push down long-term interest rates.

The rise in applications, along with signs that home prices and sales have stopped hemorrhaging, suggests mortgage rates may not fall much lower and that a rebound in housing is dependent on improvement in the labor market, strategists said on Wednesday.

The Mortgage Bankers Association said its total loan applications index rose a seasonally adjusted 10.9 percent to 493.1 in the week ended July 3, after slumping the prior week to the lowest level since November.

Last week's report was adjusted to account for the Independence Day holiday on Friday.

Average 30-year mortgage rates stayed at 5.34 percent. While up from a record low 4.61 percent in late March, the rate is below its recent peak of 5.57 percent in early June and sharply lower than 7.04 percent a year ago.

If borrowers expect mortgage rates have seen their lows, there could be another push to lock in rates before they rise. A sudden spike in home loan rates from record lows in the spring had derailed a race by homeowners to cut monthly costs by refinancing.

David Kelly, managing director and chief market strategist at JPMorgan Funds, said mortgage rates may have hit their lows, noting the Federal Reserve's unchanged stance on its plans to buy up to $1.45 billion in mortgage-related securities and $300 billion of Treasuries in order to lower borrowing costs and help revive the economy.

Treasury yields act as a benchmark for mortgage rates.

The fact that the Federal Reserve has not announced further purchases of Treasuries tells me that they are willing to let Treasury rates move up if the economy is perceived as improving, said Kelly.

Over the next month or two we'll see a lot of economic numbers which suggest that the pressure on the Fed is easing to attempt to chisel long-term rates, he added.

That would mean home loan rates may have seen their cyclical lows, Kelly said. People shouldn't sneeze at a 5-1/3 percent mortgage rate. If you want to buy, there's no better time than right now.

The Mortgage Bankers Association's seasonally adjusted refinancing index rose 15.2 percent last week to 1,707.7, after a 30 percent plunge in the prior week.

Purchase applications, which lagged refinancing demand all through the spring home sales season, rose 6.7 percent last week to 285.6.

Susan Wachter, real estate and finance professor at The Wharton School, University of Pennsylvania, said the real issue for the housing market is improvement in the U.S. unemployment rate, now at its highest level in more than a quarter century -- a view shared by many economists.

Interest rates still remain relatively low, so that's not right now the serious problem, she said. The real problem is the unemployment rate, which is still a negative and worsening force.

Housing is key to the economy, and recent signals point to decelerating declines, Wachter said. But she said interest rates could rise.

I do think the Fed if necessary can pile on more liquidity, but there's danger to doing so. It has long-run consequences which are not totally under the Fed's control, she said.

Concerns that inflation will be stoked by the Fed's aggressive moves to add liquidity to the financial system could also increase long-term interest rates.

(Editing by Leslie Adler)