WASHINGTON—The number of Americans claiming new unemployment benefits fell last week to the lowest level since 1973, signaling continued health in the labor market.

Initial jobless claims, a proxy for layoffs across the U.S., fell by 12,000 to a seasonally adjusted 215,000 in the week ended March 24, the Labor Department said Thursday. This marked the lowest level for claims since they hit 214,000 in January 1973.

“When...