WASHINGTON (Reuters) - U.S. single-family homebuilding rebounded sharply in August and permits increased, but rising new housing supply poses a challenge for builders.

Single-family housing starts, which account for the bulk of homebuilding, surged 15.8% to a seasonally adjusted annual rate of 992,00 units last month, the Commerce Department's Census Bureau said on Wednesday. Data for July was revised higher to show starts falling to a rate of 857,000 units instead of the previously reported 851,000 pace.

Some of the decline in starts in July was blamed on Hurricane Beryl.

A surge in mortgage rates in spring weighed on home sales, resulting in excess supply of newly built houses. Existing home inventory has also risen, reducing the incentive for builders to construct new houses.

Mortgage rates have since retreated to 1-1/2-year lows and could drop further, with the Federal Reserve expected to start its policy easing cycle on Wednesday. Given the supply overhang, economists do not expect a sharp increase in new construction.

A National Association of Home Builders survey on Tuesday showed homebuilder sentiment improved marginally in September after sliding for four consecutive months, but noted that "builders will face competition from rising existing home inventory in many markets as the mortgage rate lock-in effect softens with lower mortgage rates."

New housing supply is near levels last seen in early 2008. Permits for future construction of single-family homes increased 2.8% to a rate of 967,000 units in August.