The Obama administration’s latest housing scorecard reflects an improving market, with the number of underwater borrowers falling 5.8% in the first quarter to 11.4 million from 12.1 million the previous quarter.

The administration, citing data from Corelogic (CLGX), reported that a year earlier, 11.5 million borrowers were underwater.

However, the housing market remains on fragile ground.

Foreclosure starts and completions declined in May, though officials expect activity to increase in the coming months as firms lift delays in foreclosure processing. Also, the inventory of houses for sale remained low. At the current pace, it would take 6.6 months to sell the supply of existing homes on the market and 4.9 months to clear the new homes on the market.

Experts consider a six-month supply of homes to be a balanced market.

The inventory of existing homes for sale slid to 2.39 million in June from 2.47 million in May, according to data from the Department of Housing and Urban Development and the Treasury.

Home prices grew to $139,000 on average for June, compared to $135,900 in the previous month, according to Standard & Poor's/Case-Shiller data cited in the scorecard.

New home sales totaled 29,200 in June, up from 25,300 a year earlier. And existing home sales hit 364,200, up from 348,300 in the year-ago period. First-time homebuyer numbers grew to 145,500 from 138,300 in June 2011, according to the scorecard.

Foreclosure starts rose slightly to 64,100 in June from 63,900 the year before, according to the scorecard. Foreclosure completions, in contrast, fell during the same period to 54,300 from 68,900. (Click on graph to expand.)

Mortgage originations for the purchase of new homes declined to 493,000 in the second quarter from 541,800 in the year-ago period. Refinance originations rose to 1.23 million from 869,100 in that period.

Mortgage delinquency rates rose to 4.1% from 3.9% the previous month, but are below last year’s rate of 4.4%.