WASHINGTON—The number of new applications for unemployment benefits dropped last week to their second-lowest level in 14 years, the latest indication layoffs are trending lower amid generally improving economic conditions.

Initial claims for unemployment benefits fell by 36,000 to a seasonally adjusted 280,000 in the week ended Sept. 13, the Labor Department said Thursday. That was less than the 305,000 claims forecast by economists surveyed by The Wall Street Journal and placed them just above the 14-year low they hit in...