WASHINGTON, April 28 (Reuters) - U.S. single-family house prices were unchanged on a monthly basis in February, but elevated mortgage rates as the war with Iran continues could keep the dream of owning a home out of the reach of many young Americans.

The flat reading in house prices followed an upwardly revised 0.2% increase in January, the Federal Housing Finance Agency said on Tuesday. House prices were previously reported to have nudged up 0.1% in January.

Prices advanced 1.7% in the 12 months through February, after climbing 1.8% in January. A shortage of housing, mostly starter homes, is supporting annual house price growth.

The average rate on the popular U.S. 30-year fixed-rate mortgage dropped to 5.98% at the end of February as Freddie Mac and Fannie Mae expanded purchases of mortgage-backed securities.

But it shot up to 6.46% at the start of April as the U.S.-Israeli war with Iran boosted oil prices and fanned inflation fears, resulting in an increase in U.S. Treasury yields. Mortgage rates track Treasury yields. The rate averaged 6.23% last week, data from Freddie Mac showed.

Lack of housing affordability has become a hot-button issue ahead of ​the U.S. midterm elections in November. Monthly house prices increased in the South Atlantic, New England, East South Central and West South Central regions. But they tumbled 1.1% in the Mountain region and dropped 0.5% in the Pacific region. 

On a year-over-year basis, prices increased 4.2% in the Middle Atlantic region and rose 4.0% in the East South Central region. They, however, fell in the Mountain, Pacific and West South Central regions.