About one in seven American households with mortgages is behind on payments or in foreclosure, according to new data from the Mortgage Bankers Association. That is up from about one in 10 a year ago.

The group reported Thursday that 14.4% of first-lien mortgages on one-to-four-family homes in the third quarter were 30 days or more overdue or in the foreclosure process. That is the highest rate since the MBA began reporting such data in 1972, and works out to about 7.5 million households at risk of losing homes. The percentage...