WASHINGTON (Reuters) - U.S. single-family house prices increased solidly in September, which together with a resurgence in mortgage rates will further reduce affordability for many prospective homeowners.

House prices jumped 0.7% on a month-on-month basis after an upwardly revised 0.4% rise in August, the Federal Housing Finance Agency said on Tuesday. Prices were initially reported to have gained 0.3% in August.

They increased 4.4% in the 12 months through September, matching the upwardly revised rise in August. The gain in annual house prices was previously reported to have been 4.2%. The pace of increase, however, slowed from the second quarter. House prices rose at a 2.86% annualized rate in the July-September quarter after advancing at a 3.76% pace in the second quarter.

Though the Federal Reserve cut interest rates in September and earlier this month, mortgage rates have risen in tandem with U.S. Treasury yields on strong economic data and investor fears that President-elect Donald Trump's policies, including higher tariffs on imported goods and mass deportations, could reignite inflation. Mortgage rates track the 10-year Treasury note and have erased the total decline seen in September.

The average rate on the popular 30-year fixed-rate mortgage is just below 7%, having dropped to nearly 6% in September.

There were strong monthly house price gains in the Mountain, New England, East South Central and Middle Atlantic regions. Prices were unchanged in the West South Central region.

All census regions reported annual house price gains, with the Middle Atlantic region topping the list. Prices rose moderately in the West South Central region.