In the photo (R) released by China's Xinhua News Agency, security personnel surround Venezuela's President Nicolas Maduro during an incident as he was giving a speech in Caracas, Venezuela, Saturday, August 4, 2018.
Mr Rodriguez also said that the injured soldiers were being treated in hospitals while the president was meeting his ministers and military commanders.
Venezuelan President Nicolas Maduro reacts during an event which was interrupted, in this still frame taken from video.
The drones, loaded with explosives, detonated near the presidential box.
A senior US State Department official said the White House was monitoring the situation closely.
During the incident, Maduro was speaking about Venezuela's economy in an address when audio of the live television coverage was suddenly cut off.
He said the "far right" working in co-ordination with detractors in Bogota and Miami, including Colombian President Juan Manuel Santos, were responsible.
Attorney General Tarek William Saab said the attempted assassination targeted not only Maduro, but rather the military's entire high command on stage with the president.
However, Rodriguez said seven soldiers were injured in what he described as an attempt on Maduro's life.
Firefighters at the scene of the blast disputed the government's version of events.
Hundreds of thousands of Venezuelans have fled due to food and medicine shortages and hyperinflation that could reach one million percent this year, according to the International Monetary Fund.
A Colombian government source said Maduro's allegation was "absurd" and that Santos was celebrating his granddaughter's baptism on Saturday.
"The people are with the president", Rodriguez said.
Last year, the president said the new body replaced the elected legislature. One of the key reasons for the protests was the creation of the Constitutional Assembly, which aimed to short-circuit the National Assembly in which the opposition won a supermajority in 2015 elections.
"The event is evidence of desperation of ultraright leaders who, being defeated politically, continue to resort to criminal practices, and they have failed once again", Rodriguez said.