The U.S. State Department said in a statement that it stood behind the head of Venezuela's opposition-run congress, Juan Guaido, who said on Friday that he was prepared to step into the presidency temporarily to replace Maduro.
The statement was the latest in a series of Trump administration attacks on Maduro, whose inauguration to a new term as president on Thursday has been widely denounced as illegitimate.
"The people of Venezuela deserve to live in freedom in a democratic society governed by the rule of law," State Department spokesman Robert Palladino said. "It is time to begin the orderly transition to a new government. We support the National Assembly's call for all Venezuelans to work together, peacefully, to restore constitutional government and build a better future."
Pompeo spoke to Guaido earlier in the week shortly after the 35-year-old was elected to lead the National Assembly.
Pompeo told reporters traveling with him that the events taking place in Venezuela now were "incredibly important."
"The Maduro regime is illegitimate and the United States will continue ... to work diligently to restore a real democracy to that country," he said. "We are very hopeful that we can be force for good to allow the region to come together to deliver that."
The head of the Organization of American States, Secretary-General Luis Almagro, responded quickly, sending out a tweet recognizing Guaido as Venezuela's interim president.
Bolton reaffirmed the U.S. position that the May election that gave Maduro a second term was "not free, fair or credible." Bolton said "we support the courageous decision" of Guaido's declaration "that Maduro does not legitimately hold the country's presidency."
Guaido asked Venezuelans to mass in a nationwide demonstration on Jan. 23, a historically important date for Venezuelans - the day when a mass uprising overthrew dictator Marcos Perez Jimenez in 1958.
The constitution assigns the presidency to the head of the National Assembly if Maduro is illegitimate.
The military generally has remained firmly behind Maduro so far despite some reports of small-scale attempts at revolt.
A once wealthy oil nation, Venezuela is gripped by a growing crisis of relentless inflation, food shortages and mass migration.
Seventeen Latin American countries, the United States and Canada denounced Maduro's government as illegitimate in a measure adopted Thursday at the OAS in Washington.