WASHINGTON (Reuters) - U.S. construction spending unexpectedly fell in June and the prior month's data was revised lower as higher mortgage rates weighed on single-family homebuilding.

The Commerce Department's Census Bureau said on Thursday that construction spending dropped 0.3% after a downwardly revised 0.4% decline in May.

Economists polled by Reuters had forecast construction spending rising 0.2% after a previously reported 0.1% dip in May. Construction spending advanced 6.2% year-on-year in June.

Spending on private construction projects fell 0.3% in June after dropping 0.4% in the prior month. Investment in residential construction dropped 0.3% after falling 0.7% in May.

Outlays on new single-family construction projects decreased 1.2%. Spending on multi-family housing gained 0.1%. Mortgage rates surged in the spring, depressing homebuilding and sales.

Mortgage rates have since fallen and could decline further after the Federal Reserve on Wednesday kept its benchmark overnight interest rate in the 5.25%-5.50% range, where it has been since last July, but opened the door to reducing borrowing costs as soon as its next meeting in September.

Rising housing inventory, with new single-family housing supply in June hitting the highest level since early 2008, could limit any rebound in new construction.

Residential investment, which includes homebuilding and house sales, contracted in the second quarter after double-digit growth in the January-March quarter.

In June, spending on private non-residential structures like factories dipped 0.1%.

Investment in public construction projects fell 0.4% after slipping 0.2% in May.

State and local government spending was unchanged and outlays on federal government projects declined 5.4%.

(Reporting by Lucia Mutikani; Editing by Andrea Ricci)