WASHINGTON, Jan 9 (Reuters) - U.S. single-family homebuilding rebounded in October, but permits for future construction eased, signaling caution ‌among builders as new housing inventory remains ​high and demand soft.

Single-family housing ‍starts, which account for ⁠the bulk ⁠of homebuilding, increased 5.4% to a ‌seasonally adjusted annual ​rate of 874,000 units in October, the Commerce Department's ⁠Census Bureau ‍said on ​Friday. Starts dropped to a pace of 829,000 units in ‍September from a 869,000-unit pace in August.

The reports were delayed by the 43-day government shutdown. Builders are also being ​constrained ‍by higher building and labor costs because of import ​tariffs and an immigration crackdown.

Permits for future single-family homebuilding fell 0.5% to a rate of 876,000 units in October. They increased to ​a pace of 880,000 units in September from a 858,000-unit rate in August