WASHINGTON — Housing construction posted a better-than-expected increase in January which pushed activity to the highest level in six months. The solid gain raised hopes that the construction industry is beginning to mount a sustained rebound from its worst slump in decades.

The Commerce Department said today that construction of new homes and apartments rose 2.8 percent last month to a seasonally adjusted annual rate of 591,000 units. That was better than the 580,000 annual pace that economists were forecasting.

Applications for building permits, considered a good barometer of future activity, fell 4.9 percent to a rate of 621,000, but that was after two months of large increases.

In another sign of strength, today's report revised up activity in December to show builders were starting construction at an annual pace of 575,000 units during that month, much stronger than the 557,000 originally reported. Even with the upward revision, activity fell a slight 0.7 percent in December, a dip that was blamed on severe weather in many parts of the country that depressed construction activity.