WASHINGTON — The Obama administration is expected to announce Tuesday that it is expanding its plan to stem the housing crisis by offering mortgage lenders incentives to lower borrowers’ bills on second mortgages.

During the housing boom, lenders readily gave out “piggyback” second loans that allowed consumers to make small down payments or avoid fees entirely. While home prices soared, such mortgages were even extended to borrowers with poor credit scores and people who didn’t provide proof of their incomes.

But those loans, which are attached to about half of all troubled mortgages, have proved an obstacle to efforts to alleviate the housing crisis.

That’s because borrowers who are trying to get their primary mortgage modified at a lower monthly payment need the permission of the company holding the second mortgage.The new plan aims to get rid of that roadblock, said two senior administration officials, speaking on condition of anonymity because the details were not yet public.

The administration initiative, funded out of $50 billion in financial rescue money, relies on a series of payments to mortgage companies as an incentive to modify second loans at lower interest rates.

Mortgage companies would get $500 upfront for each modified loan, plus $250 a year for three years as long as the borrower doesn’t default.Similarly, borrowers would get up to $1,000 over five years applied to the principal balance of their primary mortgage, and the government would pick up part of investors’ costs as well.

The administration also plans to give mortgage companies $2,500 payments to entice them to participate in the “Hope for Homeowners” program. It was launched by the government last fall but has so far fallen flat, proving unattractive to banks required to absorb large losses.

It was supposed to allow 400,000 troubled homeowners to swap risky loans for traditional 30-year fixed-rate mortgages with lower rates. Instead only a handful of borrowers have been able to qualify, and as of earlier this spring only one loan had completed the program.Meanwhile, the faltering economy is causing the housing crisis to spread.

Nationwide, nearly 804,000 homes received at least one foreclosure-related notice from January through March, up from about 650,000 in the same period a year earlier, according to RealtyTrac Inc., a foreclosure listing firm.

And another key piece of President Barack Obama’s plan to keep borrowers from losing their homes is expected to be defeated this week in the Senate. Allowing people to seek mortgage relief in bankruptcy court is opposed by Republicans and enough Democrats to block the proposal.

Last week, Democratic aides said the prospects of an agreement looked dim.Many lawmakers remain worried that such legislation would unleash a torrent of loan defaults, ultimately driving up mortgage rates and introducing fresh uncertainty to an already ailing economy.

Congressional Democrats had championed the legislation, which passed the House in March. But the measure quickly stalled in the Senate amid a multimillion-dollar lobbying effort by banks and credit unions that said the forced easing, or “cram-down,” of mortgage terms would impose steep and unpredictable costs.

• alan zibel