By Lucia Mutikani

WASHINGTON (Reuters) - U.S. consumer prices were unchanged in July but a rise in industrial output and home building suggested a pickup in economic activity that could allow the Federal Reserve to raise interest rates this year.

Tuesday's economic reports came as influential New York Fed President William Dudley said the U.S. central bank could raise interest rates next month, citing a tightening labor market that he said was starting to spur faster wage growth.

"The strong housing starts and industrial output performance will bolster the Fed confidence that growth momentum has rebounded, potentially supporting the bias for a near-term hike," said Millan Mulraine, deputy chief economist at TD Securities in New York. "Nevertheless, with inflation continuing to miss to the downside, the case for caution remains strong."

July's unchanged reading in the Consumer Price Index followed two straight monthly increases of 0.2 percent, while in the 12 months through July, the CPI rose 0.8 percent after increasing 1.0 percent in June.

The so-called core CPI, which strips out the volatile food and energy prices, edged up 0.1 percent in July after rising 0.2 percent in each of the previous three months. The year-on-year core CPI increased 2.2 percent in July after advancing 2.3 percent in June.

The Fed has a 2.0 percent inflation target and tracks an alternative inflation measure which has been stuck at 1.6 percent since March.

NY FED RAISES POSSIBILITY OF SEPT RATE RISE

The New York Fed's Dudley told Fox Business television on Tuesday that "it's possible" for the Fed to hike rates at its Sept. 20-21 policy meeting. Atlanta Fed President Dennis Lockhart also told reporters that he was not ruling out a move next month.

The Fed raised its benchmark overnight interest rate last December for the first time in nearly a decade.

Fed officials view the labor market as either at or near full employment. Following Dudley's remarks, financial markets were placing a 58.9 percent probability of a rate increase at the Fed's December policy meeting, up from 46.7 percent late on Monday, according to CME Group's FedWatch tool. A September rate hike has been virtually priced out.

The weak inflation data, however, pushed the U.S. dollar lower against major currencies. U.S. stock prices slipped from record highs on Dudley's comments. Yields on U.S. government debt rose.

SUBDUED INFLATION SEEN TEMPORARY

With rents and healthcare costs continuing to rise, some economists do not expect July's moderation in underlying inflation to be sustained. Medical care costs climbed 0.5 percent last month, adding to June's 0.2 percent gain.

There were also increases in the costs of hospital services, doctor visits and prescription medicine. Rents increased by 0.3 percent.

But Americans got some relief from gasoline prices, which dropped 4.7 percent last month, the first decline since February.

The cost of food consumed at home fell for a third straight month, with prices for meat, eggs, dairy and cereals declining. Prices for new motor vehicles rose for the first time since February, while the cost of apparel was unchanged.

INDUSTRIAL PRODUCTION UP

In a separate report on Tuesday, the Fed said U.S. industrial production shot up 0.7 percent last month after rising 0.4 percent in June.

Production was boosted by a 0.5 percent jump in manufacturing output, the largest gain since July 2015.

Despite benign inflation, economic growth is picking up after output averaged 1.0 percent in the first half of the year.

Warmer-than-usual weather boosted utilities production by 2.1 percent. Mining output increased 0.7 percent as oil and gas drilling surged 4.9 percent, suggesting the energy-related drag on business spending was easing.

"Overall, these factors suggest the outlook for the U.S. industrial sector has improved modestly and support our expectation of healthier economic growth in the second half of 2016," said Jesse Hurwitz, an economist at Barclays in New York.

In a third report, the Commerce Department said housing starts increased 2.1 percent to a seasonally adjusted annual pace of 1.2 million units in July, the highest level since February.

Last month's increase in groundbreaking activity supports the view that investment in residential construction will rebound after slumping in the second quarter for the first time in more than two years.

Following the industrial production and housing starts data, the Atlanta Fed raised its third-quarter GDP growth estimate by one-tenth of a percentage point to a 3.6 percent annual rate.

The firming housing market is boosting home improvement retailers such as Home Depot Inc. The company on Tuesday raised its full-year earnings forecast after reporting a 6.6 percent rise in quarterly sales.

Groundbreaking on single-family homes, the largest segment of the market, rose 0.5 percent to a 770,000-unit pace in July, also the highest level since February.

Housing starts for the volatile multi-family segment increased 5.0 percent to a 441,000-unit pace. Groundbreaking on multi-family housing projects with five units or more jumped to the highest level since September 2015.

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Core inflation divergence: CPI vs. PCE graphic http://tmsnrt.rs/1QoX3pE

U.S. inflation (CPI interactive) http://tmsnrt.rs/1N6BwRs

U.S. housing starts, building permits graphic http://link.reuters.com/mek83w

U.S. industrial output, capacity utilization graphic http://link.reuters.com/var62w

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(Reporting by Lucia Mutikani; Editing by Paul Simao)