WASHINGTON, June 30 (Reuters) - U.S. single-family house prices eased on a monthly basis in April, but remained supported by a shortage of homes for sale.

House prices dipped 0.1% after an upwardly revised 0.2% rise in March, the Federal Housing Finance Agency said on Tuesday. Prices were previously reported to have edged up 0.1% in March.

The drop in monthly house prices likely reflected weak demand as the U.S.-Israel war with Iran boosted oil prices, driving up inflation and mortgage rates. The average rate on the popular 30-year fixed-rate mortgage has increased by about 50 basis points since the conflict started at the end of February, data from mortgage finance agency Freddie Mac showed. It averaged 6.49% last week.

An outright decline in house prices is unlikely. House prices increased 2.0% in the 12 months through April, after advancing 1.8% in March.

There is a national housing shortage, especially of starter homes. The National Association of Home Builders estimates the housing shortfall at about 1.2 million homes.

The U.S. Congress last week passed a bill to make housing affordable, by, among other things, restricting single-family homeownership by Wall Street investment firms and waiving or speeding up environmental reviews for construction projects.

U.S. President Donald Trump has refused to sign the bill in an attempt to pressure his fellow Republicans to pass voting restriction measures he favors.

Monthly house prices dropped 0.8% in the Mountain region. Prices also declined in the East South Central, Pacific, East North Central and South Atlantic regions. But they increased 1.0% in New England and rose 0.4% in the Middle Atlantic region.

Prices gained 0.1% in the West North Central and West South Central regions. On a year-over-year basis, prices increased in all nine census divisions, rising 4.4% in the East North Central region and advancing 4.2% in New England.