WASHINGTON—The number of Americans filing new applications for unemployment benefits fell last week to the lowest level since December 1969, offering fresh evidence of health in the labor market.

Initial jobless claims, a proxy for layoffs across the U.S., declined by 10,000 to a seasonally adjusted 210,000 in the week ended Feb. 24, the Labor Department said Thursday. That was the lowest reading for initial claims since the week ended Dec. 6, 1969.

“Claims...