Rodriguez said on VTV public television yesterday that in San Cristobal, hotbed of the movement that has seen some of the worst violence, a 44-year-old man died after being struck by a high tension cable as demonstrators carried a billboard to form a barricade.
In Maracaibo, a 33-year-old man was killed after a homemade mortar he was handling suddenly exploded.
President Nicolas Maduro's leftist government has faced a wave of near-daily street protests since February 4, with the public venting anger over soaring crime, hyper-inflation and shortages of essential goods.
Hundreds of pro- and anti-government protesters took to the streets of the capital Caracas once more yesterday.
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Opposition supporters marched to rally against commodity shortages, crime and government censorship.
"They arrest protesting students but leave criminals and thugs free. We are isolated and voiceless," said retired engineer Elias Jorge.
Marta Perez, 50, added: "We are tired of not having enough food to eat, and criminals killing our children."
Supporters loyal to the ideology of "Chavismo" espoused by Maduro and his predecessor meanwhile marched to the presidential palace to rally against the environmental impact caused by the protests.