The Federal Reserve—unfazed by recent selloffs in emerging markets or disappointing U.S. job gains in December—said it would scale back its bond-buying program for the second time in six weeks, pressing ahead with a strategy to wind down the purchases in small and steady steps.

The Fed said it would cut its purchases of Treasury bonds and mortgage-backed securities to $65 billion a month, from $75 billion, and officials suggested they would continue reducing the purchases in $10 billion increments in the months ahead. The...