The marches on Saturday were the largest mobilizations in ten days of protests triggered by the Supreme Court decision to take over legislative powers from the opposition-controlled National Assembly.
Although the court later reversed its decision, on Friday Capriles was banned from running for office for the next 15 years. Capriles narrowly lost the 2013 presidential election that brought Maduro to power. He was accused of alleged "administrative irregularities" in his post as governor of the northern state of Miranda.
Speaking at the rally on Saturday, Capriles told supporters: "Nobody can disqualify the Venezuelan people."
Human Rights Watch issued a statement saying Capriles' disqualification indicated Venezuela was "suffering from a full-fledged dictatorship" and called for action from the regional Organization of American States (OAS).
Later, a group of youths unsuccessfully tried to set fire to a Supreme Court building. While the opposition leadership condemned the violence, they blamed President Nicolas Maduro for fueling the unrest.
Further protests have been called for Monday and for April 19, after the Easter holiday, which Maduro extended by three days.
While state-controlled television failed to show reports of the demonstrations, police made social media posts of protesters, asking for information on the unidentified "generators of violence."
Protest organizers said that more than 40 people had been detained during the rallies in Caracas, in the western city of Zulia and the central states of Aragua and Carabobo. They also claimed that civilians, supported by the government, had fired on protesters in the city of Tachira.
In San Cristobal in the west, masked gunmen reportedly set off explosions, causing demonstrators to flee.
The opposition blames Maduro for an economic crisis, triggered by the fall in oil prices but accentuated, they say, by mismanagement. There are shortages of food, medicines and basic goods.
jm/ls (EFE, AFP, AP)