As unemployment rises, more borrowers need principal forgiveness on their mortgages, not just restructured loans, Citigroup Inc.’s mortgage chief said.

The comments by Sanjiv Das, president and chief executive of Citigroup unit CitiMortgage Inc., came as Citigroup issued its latest quarterly report on its own mortgage-modification efforts. Citigroup said it helped 130,000 homeowners with $20 billion in mortgages outstanding avoid potential foreclosure last quarter.

That number increased 20% from the second quarter, the bank said in its third-quarter foreclosure-prevention report issued early Tuesday; 3% of the $751 billion of mortgages Citi services were in loss-mitigation programs or in foreclosure, a one-percentage-point increase from the second quarter.

Citigroup is alone among large banks in issuing quarterly reports on efforts to help mortgage borrowers avoid foreclosure. The reports provide a glimpse into how broader national efforts are faring, a keen interest of President Obama, other politicians and community groups.

Citi said it mitigated or modified 82% more mortgages in the third quarter than in the second quarter, and 85% more than a year earlier amid rising unemployment and the impact of the government mortgage-modification program. Mitigation includes all efforts to avoid foreclosure, including nonmodification solutions such as “short sales” of homes for less than the mortgage balance.

As the main problem of the mortgage industry changes from house-price depreciation to unemployment, the mortgage market needs more programs “where there is principal reduction for borrowers with negative equity” in their home, “as opposed to just a loan restructure,” Mr. Das said.

“The solution” of the mortgage crisis “has to move into the next gear,” he said. The government’s Home Affordability Mortgage Program, or HAMP, has “not quite addressed the issue of unemployment.”

Citi already does some modifications that include principal reductions, but only very selectively to avoid raising expectations for such deals among borrowers that don’t need reductions, a spokesman said.

Also, Citi would want lenders to share any potential upside. “In such instances, the mortgage lender should share the benefits if the property rose in value,” the spokesman said.

Rising delinquencies among prime borrowers are predominantly due to unemployment, Mr. Das said. He said the government has been “very receptive and very eager” to find solutions.

Mr. Das said he expects the number of HAMP modifications to rise, but Citi might end up doing more non-HAMP modifications because the standards of HAMP are more stringent than those of banks, including Citi. (In addition, HAMP is eligible only for first mortgages.)

Rising numbers of homeowners are defaulting after their loans are modified, Citi said in its report. Redefault rates in the quarter were nearly 39%; that number compares with 29% in the second quarter.

Nevertheless, “the performance of home-equity loans started to improve” across virtually all FICO score groups, “largely driven by the restructuring of first mortgages” in HAMP, Mr. Das said.

Foreclosures initiated in the third quarter rose about 10% from the second quarter but fell about 11% from a year earlier. Completed foreclosures fell less than 1% from the second quarter and about 48% from a year earlier.

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