The State Department said in a statement that it stood behind the head of Venezuela's opposition-run congress, Juan Guaido, who said on Friday he is prepared to step into the nation's presidency temporarily to replace Maduro.
"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."
"The United States government will continue to use the full weight of US economic and diplomatic power to press for the restoration of democracy in Venezuela," he said in the statement, which was released in Abu Dhabi where Secretary of State Mike Pompeo is currently travelling as part of a nine-nation tour of the Middle East.
Pompeo spoke to Guaido earlier in the week shortly after the 35-year-old was elected to lead the National Assembly.
But he said he would need support from the public, the armed forces and the international community before trying to form a transitional government to hold new elections to replace Maduro.
Bolton reiterated the US position that the May election that gave Maduro a second term was "not free, fair or credible" and 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 January 23, a historically important date for Venezuelans - the day when a mass uprising overthrew dictator Marcos Perez Jimenez in 1958.
But the overall military so far has remained firmly behind Maduro, despite some reports of small-scale attempts at revolt.
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