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.

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 a slight 0.1 percent to an annual rate of $302.3 billion after much bigger gains over the past three months. In June, spending for office construction and hotel projects both rose but spending in the category that includes shopping centers declined.

Spending on government building projects was essentially unchanged at an annual rate of $274.2 billion in June. Government construction spending has been down or unchanged in five of the last six months. That reflects the continued restraints facing governments at all levels who are struggling to deal sizable budget problems.

For June, spending at the state and local level edged up 0.2 percent while spending at the federal level fell by 1.6 percent.

In a sign of a slight rebound in housing after a prolonged period of weakness following the boom years of the last decade, a closely watched index of home prices showed price gains in every major city in May versus April. The Standard & Poor's/Case-Shiller home price index showed increases in all of the 20 cities tracked with the biggest monthly gains being posted by Chicago, Atlanta and San Francisco.

The housing recovery is still viewed as slow and uneven. Sales of new homes fell in June after hitting a two-year high in May. Sales of previously occupied homes also fell in June but activity was still higher than a year ago.

Builders are gaining confidence, partly because they are seeing more interest from potential buyers. Builders started construction on the most new homes and apartments in four years in June.

Despite the modest gains in housing, the broader economy has weakened in recent months. Employers have added an average of only 75,000 jobs a month in the April-June quarter. That is much lower than the average of 226,000 added in the first three months of this year.

Economic growth slowed to an annual rate of just 1.5 percent in the April-June quarter, the government reported last week. That was even weaker than the 2 percent growth rate in the first three months of the year.