A 44-year-old man died when he was struck by a high tension cable as demonstrators on Saturday carried a billboard to form a barricade in San Cristobal, a center of anti-government protests.
In Maracaibo on the same day, a 33-year-old man was killed after a home-made mortar bomb he was carrying exploded, according to Rodriguez.
The Venezuelan government has faced a wave of street protests since February 4.
Nicholas Maduro, the elected socialist president, has branded the demonstrations as a plot orchestrated by the United States to overthrow his government. Many of his supporter have also held rallies, AFP reported.
Rival demonstrations were held in the capital, Caracas, on Saturday.
Supporters of Maduro and his predecessor, Hugo Chavez, meanwhile marched to the presidential palace to rally against the anti-government marches.