“Picking exact days is difficult. I’m confident that the Venezuelan people will ensure that Maduro’s days are numbered,” Mr Pompeo told CNN.
Two people died in Saturday’s clashes between civilians and troops loyal to Mr Maduro, who blocked aid deliveries.
Self-declared interim President Juan Guaidó said Mr Maduro must resign.
Mr Guaidó, who has been recognised as interim leader by more than 50 countries, has called on other nations to consider “all measures” to oust Mr Maduro after opposition-led efforts to bring in aid descended into clashes.