Homeowners and banks are accelerating sales of properties for less than the amount owed as a U.S. law that gives them a tax break expires at the end of the year.

The transactions, known as short sales, increased by 35 percent in the third quarter from a year earlier, while sales of bank-owned homes dropped 20 percent, according to a report today by mortgage data seller Renwood RealtyTrac LLC. Together, they accounted for 41.5 percent of home purchases in the quarter.

Short sales have accounted for as many as 1.1 million transactions since 2009, helping to reduce the inventory of homes owned by banks that can blight neighborhoods and flood the market. Barring a last-minute extension of the 2007 Mortgage Forgiveness Debt Relief Act, homeowners will be taxed on the forgiven principal. With Congress focused on the so-called fiscal cliff, federal spending cuts and tax-rate hikes set to kick in on Jan. 1, the law may not be extended, leading to a drop in short sales and a rise in foreclosures.

“If you’re struggling to pay your mortgage, it’s not likely you can afford an extra $25,000 or $35,000 tax bill to avoid foreclosure,” said Edward Mills, a financial policy analyst at FBR Capital Markets in Arlington, Virginia. “Mortgage forgiveness has become part of fiscal cliff politics.”

The Internal Revenue Service typically taxes forgiven debt as income to the debtor. For short sales, the average price tag was $94,896 below the mortgage on the property, according to the RealtyTrac report. Tacking that onto borrowers’ income would not only raise the amount of taxes due — it could push them into a more expensive tax bracket.

Better Outcome

Short sales are better for the real estate market than sales of bank-owned properties, said Daren Blomquist, vice president at RealtyTrac. The average price for a short sale was $186,000 in the third quarter, compared with an average bank- sale price of $161,954, which was down 7 percent from the second quarter as empty homes lost value, Blomquist said. Bank-owned properties often are unoccupied for six months or more, while short sales result in new owners moving in directly after the purchase, he said.

“The tax break going away could really stifle the upward trend in short sales we’ve seen this year, and by extension some of the rebound we’ve seen in the housing market,” Blomquist said. “People will shy away from agreeing to a principal reduction because they won’t be able to come up with additional funds to pay a new bill.”

Home Sales

Sales of homes in some stage of foreclosure accounted for 20 percent of all U.S. homes sales, the report said. The share was highest in Georgia, at 38 percent, followed by California, at 36 percent; Arizona, at 34 percent; and Nevada, at 31 percent.

Short sales of homes that weren’t in foreclosure rose 17 percent in the third quarter, the data company said, without providing a number because the figure is based on a sampling of the market. Those sales accounted for 22 percent of all U.S. sales, and were the highest in Rhode Island, at 58 percent; Connecticut, at 47 percent; and Massachusetts, at 44 percent, according to the report.

The expiration of the tax break comes at the same time that federal policies are making debt forgiveness more common. Advocates for homeowners and mortgage industry participants say the law’s expiration could jeopardize progress made this year working through the backlog of troubled loans resulting from the six-year housing decline.

Tripled Incentives

The Treasury Department in January tripled the incentives it pays lenders for mortgage modifications to as much as 63 cents for each dollar of debt written off. In addition, the five biggest U.S. lenders agreed to reduce the principal on troubled loans by about $10 billion as part of a $25 billion settlement in February of federal and state charges of abusive foreclosure practices.

Forty state attorneys general sent a letter to Congress last month urging an extension of the tax break.

“Requiring a homeowner to pay income tax on forgiven or canceled mortgage debt would make the National Mortgage Settlement much less effective,” the letter said.

Fannie Mae and Freddie Mac, the government-owned companies that back about two-thirds of all mortgages, also streamlined their short-sale processes this year.

Fiscal Cliff

The fate of the mortgage-forgiveness tax break is bound up in the negotiations over the so-called fiscal cliff, said Douglas Holtz-Eakin, chief economist to Bush’s Council of Economic Advisers in 2001 and 2002. President Barack Obama and Republican lawmakers are trading proposals on ways to avoid the more than $600 billion in U.S. spending cuts and tax-rate increases that will automatically take effect in January if Congress doesn’t act.

The mortgage debt forgiveness measure may be tacked onto the back of a broader bill that addresses the fiscal cliff, said Holtz-Eakin.

“There’s bipartisan support for extending the mortgage-forgiveness bill,” Holtz-Eakin said. “Not doing it is a recipe for bad politics.”

If the tax break isn’t extended, it’s going to come as a surprise to many homeowners currently negotiating a principal reduction with their lenders, said Elyse Cherry, CEO of Boston Community Capital, which provides foreclosure prevention aid in Boston.

“If you ask 10 people in foreclosure, most of them wouldn’t know they may have a deadline,” Cherry said. “They know about the fiscal cliff, but they don’t know they might be facing their own cliff.”

Creating roadblocks for mortgage modifications and short sales will undo much of the government’s efforts to revive the housing market by avoiding foreclosures, she said. The federal Making Home Affordable program has resulted in about 835,000 permanent modifications, according to the Treasury Department.

“We can’t afford a reversal,” she said. “It’s at cross-purposes to all the initiatives that have been put in place to combat foreclosures.”