New single-family home sales unexpectedly fell in June, but a sharp rise in prices and declining supply suggested the market for new houses was starting to stabilize, a government report showed on Tuesday.

The Commerce Department said sales fell 1.0 percent to a seasonally adjusted 312,000-unit annual rate as sales in the Northeast tumbled to a record low. Sales were also pulled down by a sharp drop in the West. May's sales pace was revised down to 315,000 units from the previously reported 319,000 units.

Economists polled by Reuters had forecast sales at a 320,000-unit rate. In the 12 months through June, new home sales rose 1.6 percent.

Despite lean inventories, recovery in the market for new homes is being frustrated by a glut of previously owned homes, which are currently selling well below the cost of new construction.

There were a record low 164,000 new homes available for sale in June. That compares to about 3.77 million used homes on the market in June, plus properties that are in foreclosure.

The scarcity of new homes is encouraging builders to break ground on new projects. Data last week showed housing starts rose to a six-month high in June.

The Commerce Department report showed the median sales price for a new home increased 5.8 percent last month to $235,200. Compared to June last year, the median price rose 7.2 percent.

The rise in prices is the latest hopeful sign that home values are starting to stabilize.

Data last week showed the median price of an existing home increased 0.8 percent to $184,300 from June last year.

At June's sales pace, the supply of new homes on the market fell to 6.3 months' worth, the lowest since April 2010, from 6.4 months' worth in May.

(Reporting by Lucia Mutikani; Editing by Neil Stempleman)

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