Last year, the European Union hit the Venezuelan vice-president and 10 other officials with sanctions over rights abuses and irregularities in the re-election of Maduro.
Maduro said he had escaped an "assassination" attempt using an explosive-laden drone during a Caracas military parade, which the government said injured seven soldiers.
Maduro accused neighboring Colombia and unidentified "financiers" in the United States of being behind the blast, while some of his officials blamed Venezuela's opposition.
The US on Monday branded the Venezuelan President a "dictator" threatening his country's democracy and imposed sanctions targeting any assets he might hold on US territory.
Luisa Ortega said on Monday that she will not recognise a new assembly voted in on the weekend, calling it an expression of "dictatorial ambition".
President Maduro called the vote for a constitutional assembly in May after a month of protests against his government, post-Venezuela's descent into crisis during its four years in power.
Accompanied by close advisors and state media, Maduro voted at 6:05 a.m. local time, far earlier and less publicly than in previous elections.