BY JEFFREY SPARSHOTT AND ERIC MORATH

WASHINGTON—Sales of previously owned homes rose to their highest level in close to four years, possibly reflecting a spike in activity as buyers look to close deals before mortgage rates rise further.

Existing-home sales rose 6.5% in July from a month earlier to an annual rate of 5.39 million, the National Association of Realtors said Wednesday. That was the best month of sales since November 2009, when a home-buyer tax credit spurred activity.

Last month’s existing-home sales were 17.2% higher than a year earlier.

The number of homes listed for sale, at 2.28 …