WASHINGTON, June 16 (Reuters) - U.S. single-family homebuilding fell to an eight-month low in May, pressured by higher mortgage rates and building material prices, suggesting the housing market could remain a drag on economic growth in the second quarter.

Single-family housing starts, which account for the bulk of homebuilding, fell 1.9% to a seasonally adjusted annual rate of 882,000 units, the Commerce Department's Census Bureau said on Tuesday. That was the lowest level since last September. Single-family homebuilding decreased 6.7% year-on-year in May.

Mortgage rates have risen as the U.S.-Israeli war on Iran drove up oil prices, boosting inflation and Treasury yields. The rate on the popular 30-year fixed-mortgage has increased more than 50 basis points since the conflict started at the end of February, data from mortgage finance agency Freddie Mac showed.

Washington and Tehran on Sunday said they had agreed terms to end ​the war and reopen the Strait of Hormuz. Permits for future construction of single-family homes rose 0.6% last month to a rate of 886,000 units. They fell 1.8% year-on-year in May.

Prior to the war, the housing market was under pressure from import tariffs, which raised prices of building materials as well as appliances. Residential investment, which includes homebuilding, has contracted for five straight quarters.

A National Association of Home Builders survey on Monday showed homebuilder sentiment deteriorated in June, blamed on "rising material costs, elevated mortgage rates and ongoing affordability challenges," that "continue to strain the housing market."

Starts for housing projects with 5 units or more, a very volatile segment, plunged 41.6% to a rate of 284,000 units in May. Multi-family housing starts tumbled 12.3% year-on-year. Overall housing starts dropped 15.4% to a pace of 1.177 million units. They decreased 8.7% year-on-year in May.

Building permits for multi-family housing projects fell 3.5% to a rate of 474,000 units last month. Overall building permits slipped 0.7% to a rate of 1.413 million units last month. They fell 0.2% year-on-year in May.