WASHINGTON — Construction of new homes fell 4.7 percent in September, the biggest decline in six months, reflecting weakness in both single-family activity and apartment building.

The September result left construction at a seasonally adjusted annual rate of 1.13 million units, the Commerce Department reported Wednesday. It was the sharpest decline since a 7.7 percent fall in March.

Homebuilding has been sliding this year, but economists remain optimistic that the low level of unemployment will soon spark a rebound in sales and construction. Even though construction activity has fallen in recent months, home building is 6.1 percent higher than a year ago.

Single-family building contracted 4.6 percent in September, while apartment construction was down 5.1 percent.

Construction activity in August declined a revised 0.2 percent, a slightly smaller drop than initially reported.