The U.S. job market showed surprising resilience in October despite a partial government shutdown for half the month, rekindling debate about whether the economy is strong enough for the Federal Reserve to rein in its signature easy-money program.

The Labor Department reported that U.S. employers added 204,000 jobs last month, defying expectations for weaker hiring amid the shutdown and a debt-ceiling fight that knocked down consumer and business confidence. The jobless rate ticked up 0.1 percentage point to 7.3% largely...