WASHINGTON (Reuters) - U.S. single-family home prices increased in August amid still tight supply, which together with elevated mortgage rates continue to keep prospective buyers on the sidelines.

House prices rose 0.3% on a month-on-month basis after gaining 0.2% in July, the Federal Housing Finance Agency said on Tuesday. They increased 4.2% in the 12 months through August after an upwardly revised 4.7% advance in July. The rise in annual house prices was previously reported to have been 4.5%.

Mortgage rates initially dropped after the Federal Reserve began cutting interest rates last month, but they have risen over the past four weeks as solid economic data forced traders to surrender hopes for another 50-basis-point rate cut next month. The average rate on the popular 30-year fixed-rate mortgage rose to 6.54% last week from 6.44% in the prior week, data from mortgage finance agency Freddie Mac showed.

Many homeowners have mortgage rates below 4.0%, reducing the incentive for them to put their houses on the market, especially if they have to buy a new place.

"The slow but continued house price growth and the effect of locked-in interest rates led to persistent housing affordability challenges," said Anju Vajja, deputy director for FHFA's Division of Research and Statistics.

There were solid monthly house price increases in the West North Central, West South Central and Middle Atlantic regions. But monthly house prices fell in the East North Central and New

England regions.

All nine census regions recorded annual house price gains, with big increases in the East North Central, New England, Middle Atlantic, East South Central and West North Central areas. There were moderate gains in the West South Central, Mountain and Pacific regions.