Citigroup on Monday joined a growing list of financial institutions offering to modify the terms of mortgages for distressed borrowers, unveiling a program to help thousands meet their monthly payments while reducing the bank’s potential for larger losses as the economy erodes.

About 130,000 mortgage customers are expected to qualify for the program, resulting in the workouts of over $20 billion of loans. Bank executives said they believed it would reduce losses by hundreds of millions of dollars, and possibly more. Like some of its competitors, Citi will also hold off foreclosing on troubled borrowers who have income enough to make their monthly payment and who make a good-faith effort to work out their loan with the bank.

Several of the nation’s largest banks have made similar offers to hundreds of thousands of homeowners with plans that may wind up helping a larger pool of troubled borrowers than the government’s plan to partly guarantee home loans. Roughly 1.5 million homes were in foreclosure at the end of June, the last month for which data is available, and economists expect more borrowers to default in the coming months as unemployment rises and home values fall even more.

JPMorgan Chase, which acquired Washington Mutual and its troubled loan portfolio, announced plans in late October to cut monthly payments by lowering interest rates and temporarily reducing loan balances for as many as 400,000 homeowners. Bank of America, which acquired the large mortgage lender Countrywide Financial, announced a similar program aimed at 400,000 borrowers as part of a settlement with state officials a few weeks earlier. And HSBC ramped up its mortgage modification effort in January, and has adjusted 61,000 mortgages so far this year.