New home sales fell 1% in June as demand for newly constructed units remained stuck in a low range during the traditional spring buying season.

The U.S. Census Bureau reported Tuesday that sales of newly constructed homes fell to a seasonally adjusted annual rate of 312,000 in June from a 315,000 rate in May.  The sales rate in April was 317,000.

Overall, new home sales are off almost 13% from a year ago. 

Tuesday's report also shows that the inventory of new homes for sale has fallen 22% over the previous 12 months to 164,000 units in June, the lowest reading since 1963.  This represents a 6.3-month supply of homes at the current sales pace.

However, this lean inventory may have perked up prices.  The Census Bureau reported the median sales price of new homes sold in June was $235,200, up from $222,400 in May.

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