The Organization of American States (OAS) on Tuesday passed a resolution to call an extraordinary assembly to vote on suspension of Venezuela's membership.
In May, Maduro was returned to power in a vote that was largely boycotted by the opposition and denounced as an unconstitutional assault on democracy by Washington and most of Venezuela's neighbours.
"Suspend Venezuela from this body", Pompeo said.
"Only real elections will allow your government to be included in the family of nations", he said.
"This is the last OAS General Assembly where the Venezuelan foreign minister participates, we criticize the OAS and we withdraw", Maduro was quoted as saying by the Globovision channel.
The top American diplomat accused Maduro of "dismantling democracy", and urged more Latin American states to join the U.S. in imposing increased economic and diplomatic sanctions on his administration.
FILE - Venezuela's re-elected President Nicolas Maduro gestures after he received a certificate given by the National Electoral Council (CNE), confirming him as victor, in Caracas, Venezuela, May 22, 2018. The Trump administration is taking aim at Venezuela's increasingly authoritarian government, calling on countries in the Western Hemisphere to step up pressure on President Nicolas Maduro at a meeting of the Organization of American States.
The Lima Group and the US had already refused to recognize the victory of Maduro in the May presidential election, saying it failed to meet "international standards of a democratic, free, just and transparent process".
Venezuelan Foreign Minister Jorge Arreaza said Venezuela rejected the assembly's decision and it would enable the United States to continue its "economic war" against Maduro's socialist government. "You don't have moral authority of any kind to try to undermine our government", Arreaza said. But under the OAS charter, it takes two years for a nation to quit the organization and officials could change their mind.
Pence made a similar request last month, when he became the first USA vice president to address the OAS since Al Gore in 1994.
Pompeo told representatives of the 35 member countries at the OAS headquarters that Maduro had moved away from constitutional order and failed to live up to its OAS responsibilities, showing "unmistakable bad faith and [exhausting] options for dialogue under current conditions".
The Lima Group is a coalition of 13 Latin American countries and Canada that has been pushing for democratic reforms in Venezuela for years.