WASHINGTON (Reuters) -U.S. single-family house prices increased in August even as supply has improved significantly, suggesting affordability would remain a challenge for many prospective home buyers.  

House prices rose 0.4% on a month-over-month basis, the Federal Housing Finance Agency said on Tuesday. Data for July was revised up to show prices being unchanged instead of dipping 0.1%, as initially reported. Prices increased 2.3% in the 12 months through August, after rising by the same margin in July.

Housing supply has risen as demand ebbed following a surge in mortgage rates at the start of the year. The inventory of existing homes jumped 14.0% in September to 1.550 million units from a year ago, data from the National Association of Realtors showed last week. A government shutdown has delayed the release of new housing inventory data for September.

Though new housing supply fell in August, it remained near levels last seen in late 2007. Higher house prices could sideline some prospective home buyers despite declining mortgage rates. A sluggish labor market is also a constraint.    

The average rate on the popular 30-year fixed-rate mortgage is at a one-year low of 6.19% after surging to 7.04% in January, data from mortgage finance agency Freddie Mac shows. That has, however, not fueled strong demand for home purchase loans. 

Economists say a lackluster labor market, marked by a stagnation in hiring, is keeping potential home buyers away.

The increase in monthly house prices in August was driven by a sharp rebound in the Middle Atlantic region. There were solid price gains in the South Atlantic, New England, East North Central, East South Central and Mountain regions. Prices fell in the Pacific and West South Central regions.

Eight of the census regions reported annual house price gains in August ranging from 0.7% in the West South Central region to 6.3% in the Middle Atlantic. House prices fell 0.6% on a year-over-year basis in the Pacific region.