WASHINGTON—The number of Americans filing applications for new unemployment benefits fell at the end of August to a nearly five-decade low.

Initial jobless claims, a proxy for layoffs across the U.S., declined to a seasonally adjusted 203,000 in the last week of August, the Labor Department said Thursday. This is the lowest level of unemployment benefit applications since the end of 1969. Though data can be volatile from week to week, the four-week moving average of claims, a steadier measure, also fell to a 49-year low, signaling...