WASHINGTON, July 28 (Reuters) - U.S. single-family house prices increased in May and could combine with higher mortgage rates ‌to make home ownership even less affordable for most ‌young people.

House prices rebounded 0.3% after an unrevised 0.1% dip in April, ​the Federal Housing Finance Agency said on Tuesday. Prices increased 2.2% in the 12 months through May after rising 2.0% in April, supported by a shortage of previously owned houses available for ‌sale, especially starter homes.

The ⁠average rate on the popular 30-year fixed-rate mortgage has increased by 60 basis points since the ⁠U.S. and Israel attacked Iran at the end of February. The rate averaged an 11-month high of 6.58% last week, data ​from mortgage ​finance agency Freddie Mac showed, ​as a fragile ceasefire ‌between the U.S. and Iran collapsed, raising oil prices and U.S. Treasury yields.

Mortgage rates track the benchmark 10-year Treasury note. The National Association of Home Builders estimates the housing shortfall at about 1.2 million units.

Monthly house prices jumped 1.4% in the ‌East South Central region and rose ​1.1% in the Mountain region. There ​were gains in the ​South Atlantic, Middle Atlantic, New England, West North ‌Central and West South Central ​regions. Prices fell ​in the Pacific and East North Central regions.

On a year-over-year basis, prices increased in eight of the census divisions, ​with significant gains ‌in the East North Central and Middle Atlantic regions. ​They fell 0.3% in the Pacific region.

(Reporting by Lucia ​Mutikani; Editing by Paul Simao)