"You'll see in the coming days a series of actions that continue to increase the pressure level against the Venezuelan leadership folks, who are working directly against the best interest of the Venezuelan people," Pompeo said. "We're determined to ensure that the Venezuelan people get their say."
He did not give further details on the nature of the planned actions.
Venezuela's information ministry did not immediately respond to a request for comment.
The Trump administration has steadily increased sanctions against officials in the leftist government of President Nicolas Maduro, accusing it of stifling democracy by jailing opposition leaders.
Last year, Washington imposed sanctions prohibiting trading new debt and equity issued by the Venezuelan government and its state oil company PDVSA. It has imposed several rounds of sanctions on government officials, including on Maduro.
Venezuela's economy has collapsed under Maduro, with annual inflation running at 200,000 percent, and staple foods and basic medicine increasingly difficult to obtain, which has led to mass emigration.
Pompeo's warning comes ahead of the annual United Nations General Assembly in New York next week attended by heads of state from around the world. Maduro has not attended the meetings since 2015 and this week said he may not attend the gathering because of concerns about his safety.
In August, two drones exploded over an outdoor rally in Caracas where Maduro was giving a speech, injuring seven soldiers and leading to the arrest of over a dozen suspects, including several military officials. Maduro described it as an assassination attempt.
(Reporting by Lesley Wroughton, editing by Rosalba O'Brien and James Dalgleish)