WASHINGTON – Another strong gain in homebuilding pushed U.S. construction spending up for a third straight month in June, a further indication that the battered housing industry is showing signs of life.

Construction spending rose 0.4 percent in June following an upwardly revised 1.6 percent gain in May that was the biggest one-month increase since December, the Commerce Department reported Wednesday.

The June advance pushed spending to a seasonally adjusted annual rate of $842.1 billion, up 12.9 percent from a 12-year low hit in February 2011. Still, the level is roughly half of what economists consider to be healthy. The construction industry has been flashing signs of improvement while other sectors of the economy have slowed.