WASHINGTON — U.S. home construction fell 6% in January but applications for building permits, which typically signal activity ahead, rose sharply.

Last month’s decline pushed home and apartment construction down to a seasonally adjusted rate of 1.58 million units in January, compared with 1.68 million in December, the Commerce Department reported today.

Single-family construction starts dropped 12.2% while construction of apartment units rose 16.2%.

Applications for building permits, considered a good sign of future activity, were up 10.4% in January to an annual rate of 1.88 million units.