The gatherings came on the eve of a deadline imposed by the European Union and major European countries for the Venezuelan leader to call “free elections” or have them recognize Guaido.
Pro-Maduro demonstrators converged in the western side of the capital city to mark the 20th anniversary of the Bolivarian revolution and the rise to power of the late Hugo Chavez.
Maduro calls for early parliamentary elections
Addressing his supporters, Maduro called for new parliamentary elections earlier than planned and reiterated the legitimacy of his presidency and his government amid mounting Western pressure for him to step down.
“They (the opposition) want to bring forward elections, let’s have elections,” Maduro said, adding he was "very ashamed to see this group of opposition coup perpetrators" take orders from Washington.
Hundreds of members of a civilian militia and public workers attended the pro-Maduro rally, many of them wearing khaki uniforms in a show of military support for the 56-year-old president.
Guaido calls for more protests against Maduro
On the other side, supporters of Guaido, who is also head of Venezuela's National Assembly, gathered at five locations around the city for a march on EU headquarters in eastern Caracas.
Carrying Venezuelan flags and blowing horns and whistles, the demonstrators called for the resignation of Maduro and an earlier than planned parliamentary election.
Addressing thousands of his supporters in Caracas, Guaido said this month “should be decisive,” and that protests would continue until his supporters achieved "freedom.”
The Venezuelan opposition leader also reiterated an appeal to the "civil and military officials" of Maduro's government to back him. "Soldier of the nation... you have a role in the recovery of Venezuela," he said.
The 35-year-old Guaido further called for another demonstration on February 12.
The rallies came a day after US Vice President Mike Pence reiterated support for Guaido, saying Washington would forgo "dialogue" and consider "all options" to help the self-proclaimed president against the legal government of Maduro.
The administration of President Donald Trump has wasted no efforts in stepping up pressure on Maduro since Guaido challenged his leadership.
Trump immediately recognized the opposition leader as the legitimate president of the oil-rich country, and soon after that Washington imposed unilateral sanctions on Venezuela's oil industry in an attempt to boost the opposition.
Maduro, who began his second six-year term as president in January, has the backing of the country’s army amid the political crisis. Reiterating support for Maduro, Venezuelan Defense Minister Vladimir Padrino said earlier this week that his soldiers were ready to die for the country.
Oil-rich Venezuela is mired in economic turmoil, with people grappling with hyperinflation, power cuts and shortages of basic items.
Caracas accuses Washington of being behind the crisis as part of a bid to topple Maduro’s government.