(Reuters) - The Federal Reserve is closely watching changes in the unemployment rate and would respond if it starts a quick climb, Fed Governor Lisa Cook said on Wednesday.

With a 4.1% unemployment rate "the labor market is still robust," Cook said at an event in Australia. "But we are very attentive to what is happening with the unemployment rate ... The situation could change very quickly and we would be responsive."

(Reporting by Howard Schneider in Washington; Editing by Sandra Maler)