Home prices were down 2.4 percent from the fourth quarter of 2010, the agency said.
To close out the year, the house price index in December rose 0.7 percent compared to November.
"While FHFA's national index shows a 2 percentage point price decline over the latest four quarters, 12 states and the District of Columbia posted price increases," said FHFA economist Andrew Leventis in a statement.
"When coupled with the fact that about half of all U.S. states saw price increases in the latest quarter, this growth adds to mounting evidence that real estate markets are seeing at least some signs of life," he said.
The agency's House Price Index tracks prices for homes with mortgages backed by either the Federal National Mortgage Association or the Federal Home Loan Mortgage Corp.
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