An extended run of modest labor market gains this year has produced little acceleration in wage growth or inflation, underscoring a puzzle that complicates Federal Reserve policy decisions looming in the months ahead.

Nonfarm payrolls rose a seasonally adjusted 156,000 in August, ​a modest slowdown from the prior two months, ​the Labor Department said Friday. When combined with June and July’s job growth, estimates of which were revised down, data show the economy still added jobs this summer at almost the exact pace that...