U.S. employers added jobs at a steady pace last month, and the unemployment rate hit a 50-year low, signaling the labor market continues to provide opportunities for Americans in search of work despite a broader economic slowdown.

The U.S. economy added 136,000 jobs in September, the Labor Department reported Friday. The jobless rate dropped to 3.5% in September from 3.7% in August, marking the lowest jobless rate since December 1969, when it also logged in at 3.5%.

Meanwhile, average hourly earnings climbed 2.9% from September 2018, a slowdown from previous...