WASHINGTON (AP) — Fewer people bought new homes in June, evidence that the housing market remains weak.

The Commerce Department says sales of new homes fell one percent in June to an annual rate of 312,000. That’s less than half the 700,000 homes sold per year that economists say is typical in healthy markets.

Sales fell to record lows in the Northeast and West. The median price of a new home rose to $235,200 in June, up 5.8 percent from May.

Housing remains the weakest part of the U.S. economy. Last year was the worst for new-home sales on records dating back a half century. Through the first six months of this year, sales are lagging behind last year’s totals.

Meantime home prices in major U.S. cities rose for the second straight month in May, propped up by an annual flurry of spring buyers. But after adjusting for such seasonal factors, prices fell in a majority of markets.

The Standard & Poor’s/Case-Shiller home-price index shows prices rose in 16 of the 20 cities it tracks.

Boston posted the biggest monthly increase, followed closely by Minneapolis and Washington. Three metro areas hit the hardest by the housing crisis — Detroit, Las Vegas and Tampa, Fla. — hit their lowest points since the recession began. Prices in Phoenix were unchanged.

The index covers metro areas that include about 50 percent of U.S. households. It rose one percent in May. But 19 of the 20 cities have seen price declines over the past year.