Applications for all government-backed mortgages will continue to be processed during a government shutdown, according to the U.S. Department of Housing and Urban Development.

HUD originally said on Friday that it would stop working on applications for loans guaranteed by the Federal Housing Administration if the lights go out in Washington. But it reversed that position over the weekend.

"The HUD Contingency plan posted on Friday mistakenly included incorrect information about a potential shutdown's impact on the FHA single-family loan program," HUD said in a statement. "FHA will be able to endorse single family loans during the shutdown. A limited number of FHA staff will be available to underwrite and approve new loans."

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HUD said it will continue processing loans "in order to support the health and stability of the U.S. mortgage market."

Loans backed by the FHA and the Veteran's Administration, as well as rural development loans backed by the United States Department of Agriculture, accounted for 45% of all mortgages used to purchase homes issued in 2012, according to the Federal Reserve. The FHA alone insures about 60,000 loans a month.

Fannie Mae and Freddie Mac, the giant government-controlled mortgage companies, had already said that their operations would be unaffected by a shutdown. Those companies pay for their operations out of the fees that they charge lenders.

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It's not clear how the FHA will still be able to handle the large load of loan applications when, according to the new contingency plan, it is planning to furlough more than 96% of staff members.

"There will be a limited number of exempted FHA staff available to underwrite and approve single family home loans," said Jereon Brown, Deputy Assistant Secretary for Public Affairs. "The underwriting and approval process will definitely be slower than normal.