WASHINGTON, April 16 (Reuters) - U.S. single-family homebuilding tumbled in March after hefty gains in the prior month, and while demand for housing remains strong, a resurgence in mortgage rates is pushing potential buyers to the sidelines.

Single-family housing starts, which account for the bulk of homebuilding, dropped 12.4% to a seasonally adjusted annual rate of 1.022 million units last month, the Commerce Department's Census Bureau said on Tuesday. Data for February was revised higher to show single-family starts rebounding to a rate of 1.167 million units instead of the previously reported 1.129 million units.

New construction remains underpinned by a severe shortage of previously owned houses for sale, with the latest government data showing 757,000 housing units on the market in the fourth quarter, well below the 1.145 million units before the COVID-19 pandemic.

A survey from the National Association of Home Builders (NAHB) on Monday showed confidence among single-family home builders unchanged at an eight-month high in April. The NAHB said "buyers are hesitating until they can better gauge where interest rates are headed."

The average rate on the popular 30-year fixed mortgage has drifted up towards 7%, data from mortgage finance agency Freddie Mac showed, as strong reports on the labor market and inflation suggested that the Federal Reserve could delay an anticipated rate cut this year. A few economists doubt that the U.S. central bank will lower borrowing costs this year.

The Fed has kept its policy rate in the 5.25%-5.50% range since July. It has raised the benchmark overnight interest rate by 525 basis points since March 2022.

Starts for housing projects with five units or more plunged 20.8% to a rate of 290,000 units. Overall housing starts plummeted 14.7% to a rate of 1.321 million units in March.

Economists polled by Reuters had forecast starts falling to a rate 1.487 million units.

Permits for future construction of single-family homes fell 5.7% to a rate of 973,000 units in March. Multi-family building permits were unchanged at a rate of 433,000 units.

Building permits as a whole dropped 4.3% to a rate of 1.458 million units. (Reporting by Lucia Mutikani; Editing by Chizu Nomiyama)