The agency said home prices rose 6.7 percent on a 12-month basis in the first quarter, which is down from the 7.1 percent annual inflation rate from the end of February.
The agency's price index reflects prices of homes with mortgages backed by either the Federal National Mortgage Association or the Federal Home Loan Mortgage Corp., better known as Freddie Mac and Fannie Mae.
"The housing market has stabilized in many areas and home building activity has strengthened in recent quarters," FHFA Principal Economist Andrew Leventis said in a statement.
"That said, labor market weakness and still-elevated foreclosure pipelines remain hindrances to a more robust recovery," he said.
From February to March, the home price index rose 1.3 percent, the agency said.
Among the nine census divisions, prices rose fastest in the Pacific division, with prices up 4.4 percent.
The slowest growth was in the Middle Atlantic division, where prices rose 0.3 percent from the previous quarter.
Among the country's 75 largest cities, Jacksonville, Fla., registered the fastest home price growth in the quarter, up 9.3 percent from the fourth quarter of 2012.
The slowest growth was in the Bridgeport-Stamford-Norwalk market in Connecticut, where prices contracted 3.5 percent quarter to quarter.