"There's more sanctions to be had. There's more humanitarian assistance, I think, that we can provide… I think we'll find other ways to make sure that food gets to the people who need it, and we will," Pompeo told the CNN broadcaster.
He noted that the "further action will be contemplated" during the Monday meeting of the Lima Group, which is a diplomatic body created in 2017 to settle the Venezuelan crisis.
The secretary of state has not ruled out the use of military force against Venezuela.
"Every option is on the table… We're going to do the things that need to be done to make sure… that democracy reigns and that there's a brighter future for the people of Venezuela," Pompeo told the Fox News broadcaster.
He added that the United States would support Venezuelan opposition leader Juan Guaido, who proclaimed himself interim president, provide humanitarian aid for Venezuela and boost the international coalition of states that are opposing Venezuelan President Nicolas Maduro.
The day before, the Venezuelan opposition tried to ensure deliveries of humanitarian aid to the country from neighbouring Colombia and Brazil, which resulted in clashes with security forces as Maduro regards the deliveries as a ploy to topple his government.