(Bloomberg) — Treasury Secretary Timothy Geithner said today that housing markets are showing “broad signs” of improvement even though they haven’t yet healed.

“We’re still living with some risk that housing is going to be a source of weakness for the broader economy,” Geithner told reporters on a conference call. Geithner said the Treasury’s mortgage-modification program now includes 500,000 households, a few weeks ahead of the administration’s target. That represents about 40 percent of the 1.2 million homeowners currently eligible for the program.

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