NEW YORK (Reuters) - U.S. home prices rose 5.1 percent in the year to August as home buyers competed for fewer properties, helped by low mortgage interest rates, some wage growth and low unemployment.

The S&P CoreLogic Case-Shiller report published on Tuesday said its 20-city index was up 5.1 percent, after a rise of 5.0 percent in the year to July. The national index has now almost recovered to the record high set in July 2006 before the financial crisis of 2008.

"All 20 cities saw prices higher than a year earlier with 10 enjoying larger annual gains than last month," David Blitzer, managing director and chairman of the Index Committee at S&P Dow Jones Indices, said.

The acceleration in home price inflation comes after other signs the housing recovery is gaining strength.

Sales of existing U.S. homes increased 3.2 percent in September from August, but the number of homes for sale has fallen nearly 7.0 percent from a year ago, the National Association of Realtors said last week. Just 2.04 million existing homes were for sale in September.

Building of new single-family houses rose 8.1 percent in September, in data published earlier by the Commerce Department, although the annual rate of 783,000 starts remains well below the historical average of more than one million annual rate of new home building.

"Demand is high and enthusiasm for homeownership remains strong, especially among all-important young, minority and would-be first-time buyers," Svenja Gudell, chief economist at real estate data provider Zillow, said.

Case-Shiller's national index, after seasonal adjustment, rose 0.6 percent month-over-month in August, while the 10-city and 20-city indexes rose 0.2 percent.

Portland, Seattle and Denver reported the strongest year-over-year increases for the seventh month in a row, with gains of 11.7 percent, 11.4 percent and 8.8 percent, respectively, as buyers were forced out of the expensive Silicon Valley area in California.

After the financial crisis of 2008, home prices plunged 35 percent from their peak in July 2006 until they bottomed out in March 2012. They have since risen to just 7.2 percent below the peak.

CONSUMER CONFIDENCE SLIPS

Consumers' perceptions of both current conditions and the six-month outlook dimmed in October, with the U.S. Conference Board's confidence index slipping to 98.6 in October, down from 103.5 in September.

Economists expected the index to hit 101.5 in October, according to a Thomson Reuters consensus estimate.

The survey, a closely followed barometer of consumer attitudes, measures confidence toward business conditions, short-term outlook, personal finances and jobs.

"Consumer confidence retreated in October, after back-to-back monthly gains," said Lynn Franc, director of economic indicators at The Conference Board.

"Consumers' assessment of current business and employment conditions softened, while optimism regarding the short-term outlook retreated somewhat. However, consumers' expectations regarding their income prospects in the coming months were relatively unchanged."

Monthly U.S. job growth slowed to an average 161,000 in August and September after gains in the previous two months and is averaging 178,000 this year, down from 229,000 in 2015.

However, unemployment remained low at 5.0 percent in September.

The Conference Board report also said the present situation index, which measures overall consumer sentiments toward the present economic situation, decreased to 120.6 from 127.9 in the prior month. The Expectations Index, which measures sentiments for the next 6-months, declined to 83.9 from 87.2 in September.

(This version of the story , corrects organization name to "Zillow" in the 7th paragraph)

(Writing by Clive McKeef; Editing by Chizu Nomiyama)