Opposition leaders have called for Maduro to be ousted by constitutional means, accusing him of dragging the country close to economic ruin.
Despite having lost control of the National Assembly legislature Maduro dug in his heels as he rallied supporters near the Miraflores presidential palace.
The rally commemorated a failed 1992 coup attempt by his predecessor Hugo Chavez, whom he hails as founder of the government's socialist "revolution."
"The people must not allow the oligarchy to cut short this beautiful revolution," he told the crowd of thousands yesterday.
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On Tuesday a small group of lawmakers presented a proposed constitutional amendment to cut Maduro's mandate short by two years and call a general election by the end of this year.
The lawmakers were from the Radical Cause party, a minority member of the opposition MUD coalition. The MUD took control of the legislature last month after voters fed up with economic hardship turned on Maduro in elections.
The resulting political standoff has raised fears of violence in the South American country, where 43 people died in anti-government riots in 2014.