WASHINGTON—U. S. new-home sales in September recorded the largest single-month increase since 1992, a sign the market remains resilient despite two major hurricanes and a continuing inventory shortage.

Purchases of newly built single-family homes—a narrow slice of all U.S. home sales—increased 18.9% to a seasonally adjusted annual rate of 667,000 in September from the previous month, the Commerce Department said Wednesday. That put new home sales at the highest level since October 2007.

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