WASHINGTON — Applications for home building permits, a key gauge of future construction, fell in September by the largest amount in five months — a discouraging sign for the housing industry. A rebound in housing is needed to support a broader economic recovery.

Representatives for the industry told a congressional panel Tuesday that the $8,000 tax credit for first-time buyers needs to be extended and expanded to ensure the housing sector will emerge from the recession.

The Commerce Department said construction of homes and apartments rose 0.5 percent last month to a seasonally adjusted annual rate of 590,000 units. That was a weaker showing than the 610,000 economists had expected.

The applications for building permits fell 1.2 percent, the second setback in the past three months and the biggest decline since a 2.5 percent drop in April. It likely means construction will weaken a bit in coming months, partly because builders had accelerated projects to complete them before the tax credit expires Nov. 30.

The industry also faces other challenges, including record levels of home foreclosures and unemployment that is currently at a 26-year high of 9.8 percent and not expected to peak until next summer, said Sal Guatieri, an economist at BMO Capital Markets.