WASHINGTON – The number of foreclosed homes rose over the summer after fewer people at risk received assistance lowering their monthly mortgage payments, a new report shows.

About 470,000 homeowners received help either directly from banks or through government programs in the July-September quarter, according to a report released Wednesday by the Office of the Comptroller of the Currency and Office of Thrift Supervision. That’s a 17 percent drop from the previous quarter and a decline of 32 percent from the same period a year earlier.

At the same time, the number of completed foreclosures rose to nearly 245,000 in the third quarter, an 11.2 percent increase from the previous three months, the report said.

The report only covers the 64 percent of mortgages held by national banks and thrifts.

Mark Zandi, chief economist at Moody’s Analytics, estimates that there will be 1.8 million foreclosed homes in the United States this year, and that the numbers will be even higher in 2011. Moody’s estimates that foreclosures should peak next year at 2.1 million, Zandi said.

A spike in foreclosures is a major reason why home prices fell in 20 of the largest U.S. metropolitan areas in October from September, the first time that has happened since February 2009.

Banks have already sorted through most delinquent borrowers and decided whether to modify their mortgages, federal officials say. “The universe of eligible borrowers who have not already been evaluated is being exhausted,” said Bryan Hubbard, a spokesman for the OCC.

Many troubled borrowers owe more on their homes than the mortgages are worth, a situation known as being “under water.” Many banks don’t want to modify those mortgages, analysts said, because that would require them to write off a portion of the loan.

The Obama administration’s central effort to prevent foreclosures, the Home Affordable Modification Program, saw an even steeper drop in the third quarter. Only 59,000 loans were modified under the program, down nearly 46 percent from the previous quarter.

The federal program has fallen far short of its goals. Administration officials initially said it would help 3 million to 4 million people avoid foreclosure. But a congressional panel estimated earlier this month that it would likely end up modifying about 700,000 to 800,000 mortgages.