A year after five of the nation’s biggest banks reached a pact with state and federal officials over claims of vast foreclosure abuses, the banks are taking credit for giving more than half a million struggling homeowners roughly $45.8 billion in relief.

But despite the banner numbers released Thursday in a report by Joseph A. Smith, the independent overseer of the settlement, thousands of homeowners are still not getting the help they need to save their homes from foreclosure, according to interviews with housing advocates and homeowners facing foreclosure.

Just fewer than 71,000 borrowers, or 13 percent of the total borrowers helped so far, received assistance on their primary mortgage, which has been the main source of defaults and foreclosures through the housing crisis. But more than 170,000 homeowners received assistance on their second mortgage, which typically is a home equity line of credit that borrowers can tap for cash.

Even though addressing second mortgages does offer some relief to homeowners, in a troubling number of instances the banks are not providing any help with the first mortgage, the housing advocates said. That leaves the homeowners still in jeopardy of losing their homes, while giving banks credit for restructuring loans or wiping out debt under the settlement.

“The second-mortgage forgiveness is basically a loophole, which allows the banks to continue foreclosures unabated,” said Elizabeth M. Lynch, a lawyer at MFY Legal Services in New York.

Based on the monitor’s report, it is impossible to tell how many homeowners who received help on their second mortgage are still facing foreclosure on their first mortgage. Lynch and other advocates estimate that thousands of homeowners across the country are in that predicament.

Banks say they are actively working to assist homeowners and to fulfill all their obligations under the settlement. And Shaun Donovan, the secretary of Housing and Urban Development, which helped broker the deal with the five banks, said Thursday that the settlement had already “exceeded expectations.”

Smith said, “I believe we have made progress, but I know that there is much more work to be done.”

At its outset, the settlement was trumpeted as a way to hold banks accountable for foreclosure abuses and help homeowners harmed when the housing bubble burst, sending the housing market to its lowest level since the Great Depression. As of early 2012, roughly 4 million Americans were in foreclosure since the start of 2007, with abandoned properties marring states including Arizona, California and Florida.

The deal with the five largest servicers — Ally Financial, Bank of America, Citigroup, JPMorgan Chase and Wells Fargo — arose from a sweeping investigation by the 50 state attorneys general after revelations in 2010 that banks were churning through hundreds of foreclosure documents without examining them for accuracy.

Initially, the banks resisted reducing mortgage debt, but the attorneys general insisted that debt reduction was critical to the plan. Under the terms of the settlement, the banks receive a variety of credits based on the kind of relief that they provide. For example, banks that offer short sales to homeowners earn at most 45 cents on the dollar.

The bulk of the relief, according to the monitor’s report, comes from short sales, which housing advocates say do not actually keep homeowners in their properties. In the sales, banks agree to let homeowners sell their houses for less than the outstanding debt owed. Short sales are among the simplest form of relief, particularly because they are a palatable alternative for the banks, which typically incur lower losses on the sales than foreclosures. Through short sales, banks forgave about $19.5 billion in debt on an estimated 169,000 properties, according to the report.

Banks are modifying or forgiving second mortgages at a fast clip, according to the report, but they are far more reluctant to write off first-mortgage debt. The banks took credit for modifying or wiping out roughly $7.4 billion in debt on first mortgages held by 70,810 borrowers. In total, banks provided about $11.6 billion of relief on second mortgages, assisting 170,339 borrowers.