More Americans bought homes in September, many for the first time, despite a persistent shortage of properties for sale.

The National Association of Realtors said Thursday that sales of existing homes rose 3.2 percent from August to a seasonally adjusted annual rate of 5.47 million, the strongest pace since June. Sales rose across the country: 5.7 percent in the Northeast, 5 percent in the West, 3.9 percent in the Midwest and 0.9 percent in the South.

The supply of available homes stood at 2.04 million units, down 6.8 percent from a year ago. Tight inventories drove the median price of existing homes up 5.6 percent from a year ago to $234,200.

The institutional investors who bought up homes in recent years have continued to rent them out rather than putting them on the market. Moreover, homebuilders have not aggressively stepped up construction. The Commerce Department reported Wednesday that home construction fell 9 percent in September to the slowest pace in 18 months.

But buyers have been lured into the market by mortgage rates that remain near historic lows. Mortgage giant Freddie Mac said Thursday that the rate on a 30-year, fixed-rate mortgage rose to 3.52 percent, still close to the record low 3.31 percent from November 2012.

The association said first-time home buyers accounted for 34 percent of the purchases, the most since July 2012.

"What is lacking is inventory," said the association's chief economist, Lawrence Yun. "If we had more, we would sell more ... Home builders need to ramp up construction."