The death toll since April - when the protests intensified after Maduro's administration and the courts stepped up efforts to undermine the opposition - is at least 36, according to prosecutors.
Valencia has become one of the flashpoints of looting and clashes which have also seen violence at daily mass demos in the capital.
Among the opposition's demands are for the government to allow the delayed state elections to be carried out and the 2018 presidential election to be brought forward.
Having failed to trigger a referendum on his rule previous year, the opposition is calling for delayed state gubernatorial elections to be held as soon as possible, and for the next presidential election slated for 2018 to be brought forward.
The White House confirmed Saturday that H.R. McMaster, the United States national security adviser, had met with Julio Borges, the president of Venezuela's opposition-led National Assembly, for talks on how to resolve the issue.
Leopoldo Lopez Sr., right, father of Leopoldo Lopez, and his daughter Diana Lopez, express concern for the jailed Venezuela opposition leader in Madrid, Spain on Friday.
This week Maduro announced the installment of a constituent assembly, which will have the ability to write a new Constitution and to overrule any existing public power in Venezuela, including the National Assembly.
"We are deeply concerned about the Maduro government's violent crackdown on protesters in Venezuela", the statement said.
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In addition, this alert applies to all encounters with federal, state, county law enforcement including local police and sheriffs.
These competing marches on Saturday will likely further stoke tension in Venezuela, as the opponents continue to hold Maduro responsible for the country's political, economic and social crisis.
Saturday's protesters, led by opposition leaders and lawmakers, marched to the Interior Ministry to denounce "repression" over the past month as demonstrators have been hit with tear gas by security forces.
The president says the crisis is a US-backed conspiracy.
The government, however, insists that the protests are incited by Washington in a persisting bid to remove Maduro from power, accusing opposition elements of hiring armed gangs to confront and attack security forces.
Venezuela, despite having the world's largest oil reserves, is facing the worst economic crisis in its history with the population suffering severe food and medicine shortages amid triple-digit inflation.
"They are mobilised as if this was a war", said opposition leader Henrique Capriles, broadcasting from the scene via the Periscope app favoured by protest leaders. The family's lawyers said Friday that at least two opposition leaders with Spanish passports are being hel.
The ICRC didn't immediately respond to emailed questions about the lawyers' request.
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