Washington will present a draft UN resolution aimed at recognizing the opposition leader, revoking the credentials of Maduro's UN envoy and appointing Guaido's representative as the ambassador to the world body, Pence told the council.
"The time has come for the United Nations to recognize interim president Juan Guaido as the legitimate president of Venezuela and seat his representative in this body," Pence said.
Maduro shot back by saying in a televised speech that he had seen Pence "making a fool of himself in the United Nations Security Council" with his appeal.
"I cannot understand his arrogance and self-importance, his racial supremacism," Maduro said.
The Socialist president accused Washington of threatening a "military invasion" after Pence reiterated that "all options are on the table".
The United States is among some 50 countries that recognize Guaido, the opposition leader who declared himself interim president in January in a bid to replace Maduro, whom he has branded as illegitimate.
Maduro has maintained control with support from the military, Russia and China. Russia last month sent troops to Caracas, raising tensions between Washington and Moscow.
Pence argued that Maduro had brought "deprivation" to Venezuela and that without action, "chaos and suffering will only spread" to the region, already faced with an influx of millions of migrants.
- Another blackout -
Venezuela was plunged into another major blackout on Wednesday leaving large parts of the country without power as Maduro met with the head of the Red Cross and agreed to receive international aid.
"We confirm our readiness to establish cooperation mechanisms for international assistance and support," Maduro posted on Twitter after meeting ICRC president Peter Maurer.
Maduro has denied that his country faces a humanitarian crisis and blames US sanctions for Venezuela's economic problems, but Guaido has pointed to corruption and mismanagement by the Caracas government for the crisis.
Communications Minister Jorge Rodriguez said late Wednesday that power had been restored throughout the country, less than 24 hours after the latest blackout.
"We are now providing service throughout the country," Rodriguez said on state television.
Power returned progressively to the capital Caracas throughout Wednesday morning, though some areas in the west of the country were still reporting problems.
Guaido had called for street protests on Wednesday to keep the pressure on Maduro to step aside.
At the council, Pence said: "The United States of America will continue to exert all diplomatic and economic pressure to bring about a peaceful transition to democracy in Venezuela, but all options are on the table."
After appealing for UN recognition for Guaido, Pence turned to Venezuela's Ambassador Samuel Moncada who was seated in the council chamber and said: "With all due respect Mister Ambassador, you shouldn't be here."
"You should return to Venezuela and tell Nicolas Maduro that his time is up. It's time for him to go."
Moncada accused the United States, backed by Britain, of working to destroy his country's economy. "We must stop this war by Donald Trump," he told the council.
The Organization of American States on Tuesday recognized Guaido's envoy, Gustavo Tarre, as Venezuela's representative to the regional group.
- Russia denounces regime change -
A draft resolution recognizing Guaido would certainly be vetoed by Russia at the Security Council.
Pence indicated to reporters that the measure would be brought to the 193-nation General Assembly, where vetoes do not apply.
A bid by the United States to win support for elections failed at the council in February, after Russia and China resorted to their veto power to block the measure.
Russian Ambassador Vassily Nebenzia denounced "an attempt to change the regime in Venezuela" and warned that "external players are a direct threat to Venezuela itself."
The United States called the council meeting after a UN report detailed the heavy toll of the crisis from the collapse of Venezuela's oil economy.
Seven million people -- 25 percent of Venezuela's population -- are in need of humanitarian aid, lacking basic access to food and medical care, UN aid chief Mark Lowcock told the council.
Malnutrition rates have trebled over the past five years, particularly affecting children under five and power outages are worsening access to clean water, threatening a major spread of disease.
More than 3.4 million people have left the country and that figure is expected to reach five million by the end of the year.
"There is a very real humanitarian problem in Venezuela," said Lowcock.
US Secretary of State Mike Pompeo is due to travel to the border in Colombia on Sunday to highlight the plight of refugees.