A teenager died in the capital Caracas and a woman was killed in San Cristobal, near the Colombian border.
Tens of thousands of people have taken to the streets to demand new presidential elections and the release of jailed opposition politicians.
President Maduro has accused the opposition of attacking the police and looting shops.
He said more than 30 arrests had been made. Supporters of the government are holding a rival rally in Caracas.
Despite having the world's largest proven oil reserves, Venezuela has suffered for several years from high inflation, rampant crime and a shortage of basic goods.
What is behind the turmoil?
The protests taking place across the country were expected to be the biggest in three years, putting extra pressure on President Maduro to negotiate with the opposition and find a way of easing the country's economic crisis.
Anti-government protesters have described it as Venezuela's "second independence day".
Elections are not due until 2019, but the opposition says the country is on the verge of collapse. Inflation is expected to top 700% this year, the IMF says.
The latest crisis was triggered by last month's Supreme Court decision to officially take over power from the opposition-controlled parliament.
The Supreme Court reversed its decision after three days, but it was too late to prevent a new wave of protests.
Venezuela has now seen weeks of clashes between demonstrators and the police. The latest deaths bring the number killed to at least seven, with many more injured.
(Demonstrators want new elections and the release of opposition politicians)