State television in Venezuela showed President Maduro abruptly cutting short a speech on Saturday, Aug. 4, causing hundreds of soldiers present to break ranks and scatter.
A video shows Flores wince, and both she and Maduro look up after an unidentified sound.
Just after the explosions, the cameras turned to a wide shot of uniformed military officers standing at attention in neat lines as they broke rank and began running. The government blamed the attack on Colombia and the U.S. state of Florida, which is inhabited by many exiled Venezuelans.
The parade Maduro attended was to mark the one-year anniversary of the Constitutional Assembly, a legislative body packed with Maduro loyalists that arrogated powers from the opposition-ruled National Assembly.
But, the wire service adds, firefighters at the site of the explosion are disputing the government's account of what it called an "attack".
Bolivian President Evo Morales later posted a message of support to the victims of the attack.
"The investigation has already produced evidence that this was an attempt against the life of President Nicolas Maduro, but he is completely unharmed".
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Rodriguez said there was "an explosive charge. detonated close to the presidential podium" and in several other spots along the parade held in central Caracas.
A senior US State Department official said the White House was monitoring the situation closely.
Leftist Maduro, who replaced President Hugo Chavez after his death in 2013, has linked the attack to Colombia and the U.S.
However, seven members of the Venzuelan national guard were injured and are being treated, Mr Rodriguez said.
Elster tweeted, "Unconfirmed reports say it was an assassination attempt of Maduro by a drone, unclear if there is any casualties in this incident".
Venezuela's soaring inflation is predicted to top 1 million percent by the end of the year, economists at the International Monetary Fund recently predicted.
Maduro, who escaped unhurt in the incident, said "everything points" to a right-wing plot against him and also claimed arrests have been made in the case.