Home prices and sales remained fragile in January even as housing inventory levels and foreclosure starts improved during the same month, the Obama administration said in its latest Housing Scorecard Report.

Inventories of existing homes for sale declined from 3.2 million in the second quarter of 2011 to 2.4 million in the fourth quarter, according to data from the U.S. Department of Housing and Urban Development and the Treasury.

Overall, housing results were a mixed bag, the scorecard said. Inventory levels improved in the last two quarters while the number of housing units held off market fell from 3.9 million in the first quarter to 3.6 million in 4Q, the scorecard said. Foreclosure starts also fell in December, suggesting some signs of improvement.

Still, home prices are weak and foreclosure completions edged higher.  

Home prices hit $138,500 on average for November 2011, compared to $140,300 in October 2011, according to Case-Shiller data cited in the report. New home sales hit 25,600 in December 2011, down from 27,600 a year ago. Meanwhile, the number of existing home sales hit 384,200 in December 2011, up from 370,800 in the year-ago period. First-time homebuyer numbers grew to 204,900 in December 2011, up from 196,000 in November 2011, according to the scorecard.

Foreclosure starts fell to 58,300 in December 2011, from 71,700 in November 2011. Foreclosure completions declined during the same period hit 61,800 in December 2011, up from 56,100 in the month before that.

While mortgage originations for the purchase of new homes declined to 431,500 from 498,000 in the year-ago period, but refinance originations rose to 1.3 million in 4Q from 950,000 during 3Q. Mortgage delinquency rates were mostly falling, dropping to 4.4% in December from 4.7% in the year-ago period.