WASHINGTON — Another strong gain in homebuilding pushed US construction spending up for a third straight month in June.

The construction industry has been flashing signs of improvement while other sectors of the economy have slowed.

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.

For June, the strength came from a 1.3 percent increase in spending on housing, the fifth gain this year.

The housing gain pushed activity in this category to an annual rate of $265.6 billion. Spending on private nonresidential building projects edged up 0.1 percent to an annual rate of $302.3 billion after much bigger gains over the past three months.