Pro-government officials frequently blame power outages on Venezuela's opposition, accusing them of attacking power substations with Molotov cocktails, though they rarely provide any evidence.
Thousands of commuters flooded into the streets because subway service was stopped.
"They think they can wear us down, but there's no way they can contain a population that has chose to end the usurpation", added the leader of the opposition-controlled legislature, who is recognised as Venezuela's interim president by more than 50 countries.
"We can't take in any more corpses", an employee said on condition of anonymity.
The blackout was reported to have hit 22 of 23 states, striking during the peak of evening rush hour Thursday, sending thousands of people on long nighttime treks home through some of the world's most violent streets.
"We want to march!"
At a competing march organized by the Socialist Party to protest what it calls USA imperialism, Maduro blamed the outages on "electromagnetic and cyber attacks directed from overseas by the empire".
President Nicolás Maduro's Government has largely ignored Guaidó, apparently hoping the opposition movement will exhaust itself, as previous such efforts have.
Local power outages continue to be chronic, particularly in the sweltering western state of Zulia where residents complain of days without power or with limited electricity and voltage fluctuations that damage appliances.
The Venezuelan capital Caracas was in near-darkness on March 8, 2019 during the worst power outage in the country's history. "The little food we have is going bad". I'm going to the march because we need change.
Valeria Castillo, a 43-year-old actress, told Al Jazeera she briefly "escaped" her home where she takes care of her ailing parents to attend an opposition rally in the capital.
As well as communications, water pumps have failed, food is rotting in fridges, businesses are shuttered and transport is virtually non existent.
"We're not offering services and we don't have any patients staying here because the generator is not working", said Chiquinquira Caldera, head of administration at the San Lucas clinic in the city of Maracaibo, as she played a game of Chinese checkers with doctors who were waiting for power to return.
Guaido's declaration has intensified the crisis in Venezuela, home to the world's largest oil reserves, which has suffered more than four years of recession, hyperinflation and widespread shortages of basic goods.
Venezuela's electrical system was once the envy of Latin America but it has fallen into a state of disrepair after years of poor maintenance and mismanagement.
"I share the feeling of despair, I have lost relatives due to the lack of medicine", said Mr Guaido, who told supporters that "there's no other option to get out of this without street mobilization". Several columns of security forces moved on motorcycles.
Ecuador's foreign ministry issued a statement claiming 79 Venezuelans had died as a result of the power cut, which Rodriguez denied.
Critics blame the government for failing to invest in maintaining the electrical grid, although the government often points the finger at external factors when the lights go out. It gave no details.
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