State attorneys general are descending on Washington again this week for negotiations with federal regulators and the nation’s largest mortgage servicers over the purpose of a multibillion-dollar fund aimed at helping troubled borrowers.

The idea behind the yet-to-be-created fund, the size of which remains in flux but could eclipse $20 billion, is to punish the servicers for their shoddy foreclosure practices, which came to light in the fall, and to put that money toward keeping struggling homeowners in their homes.

But deciding how to do that remains a complicated, contentious and politically fraught task.

One option, said people with knowledge of the talks, would be to use a portion of the money to write down the principal balance for some beleaguered homeowners — a controversial approach that, bank representatives argue, raises questions of fairness and poses logistical hurdles for the industry.

Another option would be to dole out part of the funds to an array of state-run aid programs, mediation services, foreclosure hotlines and other efforts to help homeowners. But that approach also presents questions about how to allocate the money fairly and who would make that decision.

Other questions remain, such as how much in penalties each individual bank would have to pay and whether some of the money also will be set aside to compensate homeowners who suffered abuses such as wrongful foreclosures.

Even as government officials and bank representatives wrestle over the parameters of the fund, they plan to continue negotiations over large-scale changes to practices within the servicing industry.

On Friday, state attorneys general and federal regulators submitted to the mortgage servicing firms a revised version of the original 27-page term sheet that they put together this year, people familiar with the talks said.

The original proposal would require servicers to provide a single point of contact for borrowers looking to modify their loans and to do away with the “dual-track” problem in which homeowners sometimes receive foreclosure notices as they are negotiating modifications to their loans.

Government officials and banking representatives said the most recent term sheet includes items on which they have found common ground, but they acknowledged that the two sides remain far apart on key issues, such as reducing the loan balances of troubled borrowers.

The current settlement talks grew out of widespread problems within the mortgage servicing industry — including instances of forged foreclosure documents and flawed paperwork — that surfaced in the fall and prompted federal officials and the state attorneys general to join forces against the industry’s largest players.

Last month, the Office of the Comptroller of the Currency and other federal banking regulators announced a separate deal with financial firms that requires them, in part, to hire consultants to determine whether any borrowers were harmed by sloppy foreclosure practices and reimburse them for any damage. Some critics called that settlement, which did not include fines, too lenient.

Meanwhile, leaders of the 50-state coalition and other federal agencies, such as the Justice Department and the Department of Housing and Urban Development, forged ahead with their own settlement.

But even keeping that alliance together has proven tricky. Oklahoma’s attorney general, who opposes forcing servicers to reduce the principal on mortgages of borrowers who owe more than their properties are worth, has said he is prepared to break ranks. Other Republican attorneys general also have voiced concern about the original proposed terms, including Ken Cuccinelli II of Virginia.

This week’s negotiations are expected to include Iowa Attorney General Tom Miller and Illinois Attorney General Lisa Madigan, among others, as well as HUD and Justice officials and representatives of various banks, including Bank of America and Wells Fargo. The talks are scheduled to begin Tuesday, one government official said.