WASHINGTON—Sales of new homes in the U.S. slumped for the fourth-consecutive month and inventories swelled to the highest level in years, suggesting the housing market is falling deeper into a weak stretch.

Purchases of newly built single-family homes—a relatively narrow slice of all U.S. home sales—fell 5.5% to a seasonally adjusted annual rate of 553,000 in September, according to fresh data from the Commerce Department. This is the slowest rate in about two years. Meanwhile, inventory rose to a 7.1 months’ supply, the highest...