WASHINGTON (Reuters) - U.S. single-family homebuilding and permits fell in April amid a resurgence in mortgage rates, but new construction remains supported by an acute shortage of houses for sale.

Single-family housing starts, which account for the bulk of homebuilding, slipped 0.4% to a seasonally adjusted annual rate of 1.031 million units last month, the Commerce Department's Census Bureau said on Thursday.

Data for March was revised higher to show single-family starts falling to a rate of 1.035 million units instead of the previously reported 1.022 million units. Housing starts increased 17.7% year-on-year in April.

The average rate on the popular 30-year fixed mortgage pulled back from a five-month high of 7.22% to 7.09% last week, data from mortgage finance agency Freddie Mac showed, as easing labor market conditions put two rate cuts from the Federal Reserve this year back on the table.

The rise in mortgage rates over the course of April and the first week of May caused confidence among homebuilders to slump this month. The National Association of Home Builders also expressed concerns on Wednesday about recent regulations requiring the Department of Housing and Urban Development and the Department of Agriculture to insure mortgages for new single-family homes only if they are built to the 2021 International Energy Conservation Code. It said the regulations would increase the cost of construction.

The nation is facing a severe housing shortage, which should keep new construction supported. Government data showed there were 728,000 housing units on the market in the first quarter, well below the 1.145 million units before the COVID-19 pandemic.

Starts for housing projects with five units or more soared 31.4% to a rate of 322,000 units in April. Overall housing starts increased 5.7% to a rate of 1.360 million units.

Economists polled by Reuters had forecast starts rebounding to a rate of 1.420 million units.

Permits for future construction of single-family homes dropped 0.8% to a rate of 976,000 units in April. Multi-family building permits tumbled 9.1% to a rate of 408,000 units.

Building permits as a whole fell 3.0% to a rate of 1.440 million units.