WASHINGTON (Reuters) - U.S. single-family homebuilding fell in May amid continued high mortgage rates.

Single-family housing starts, which account for the bulk of homebuilding, declined 5.2% to a seasonally adjusted annual rate of 982,000 units last month, the Commerce Department's Census Bureau said on Thursday.

Data for April was revised higher to show single-family starts rising to a rate of 1.036 million units instead of the previously reported 1.031 million units.

The average rate on the popular 30-year fixed mortgage has continued to pull back after reaccelerating over 7% again in April and May. It eased to 6.95% 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.

Permits for future construction of single-family homes fell 2.9% to a rate of 949,000 units in May.