WASHINGTON — The number of Americans who bought previously occupied homes rose last month. But the National Association of Realtors says it overstated about 3.5 million sales during and after the Great Recession, showing the housing market remains much weaker than previously thought.

The private trade group says sales rose 4 percent last month to a seasonally adjusted annual rate of 4.42 million. That’s below the roughly 6 million sales a year that economists say are consistent with a healthy housing market. But it’s ahead of 2008’s revised sales, now considered the worst in 13 years.

The nearly 4.2 million homes sold last year are far fewer than the nearly 7.1 million sold at the peak of the housing boom in 2005.

The trade group revised down its sales from 2007 through October more than 14 percent, from 24.8 million to nearly 21.3 million. Among the reasons for the lower figures, the Realtors group says: changes in the way the Census Bureau collects data, population shifts and some sales being counted twice.