Power was restored to some areas of the country over the weekend but - with residents and businesses fearing that refrigerated food will spoil - service was patchy and power often lasted just a few hours before dropping out again.
Guaido headed an emergency session of the opposition-majority National Assembly to force the issue of a "state of alarm."
But even that fell victim to the blackout, as the partly-restored electricity supply failed an hour into the meeting.
(The New York Times) Source: The New York Times
"We cannot turn away from this tragedy our country is going through," the 35-year-old National Assembly leader, who in January declared himself interim president, triggering a power struggle in the oil-rich South American country of 30 million, said.
Businesses and schools remained closed as President Nicolas Maduro extended an order issued when the blackout began on Thusday.
In any event, the lack of public transport made travel difficult, even in Caracas.
The situation on the ground was still confused as Maduro battled to restore power and maintain the upper hand in his struggle with Guaido.
A ball of flame flared across the darkened sky over southeastern Caracas in the early hours of the morning when the Humboldt power station erupted in a massive explosion, increasing the chaos in an area where looting was reported on Sunday.
"I felt like I was in a horror movie," Carolina Molina, who witnessed the blast from her window, said.
State-owned electricity company Corpoelec declined to comment on the explosion.
The fire that followed the blast was still smouldering by mid-morning. A metal beam holding one of the huge transformers had melted and a permiter wall had been blackened, AFP reporters said.
'State of alarm'
Guaido - recognized by more than 50 countries as interim president - has no means to enforce a "state of alarm" as the army, police and civil service remains in Maduro's hands.
But Guaido hopes a declaration by the National Assembly would open the door to foreign intervention in the country in the name of delivering humanitarian aid.
He told supporters at a rally on Saturday he was ready to authorize a foreign military intervention.
Maduro has shut Venezuela's border to keep out humanitarian aid, dismissing it as a precursor to a US military "invasion".
Juan Guaido, Venezuela's interim president. Source: AAP
Maduro, who has blamed the blackout on US "sabotage" of the country's main hydroelectric complex at Guri, said a massive amount of food aid, water and fuel would be distributed on Monday.
He ordered that hospitals - where patients were languishing without proper treatment, and where at least 15 people reportedly died due to a lack of kidney dialysis treatment - should be given top priority.
Last month, Maduro used the military to block an opposition bid to bring in more than 250 tons of supplies over land from Colombia and Brazil.
On Sunday, the embattled president - who has presided over a calamitous economic collapse that has left people in need of basic food and medicine - vowed not to back down.
"This macabre strategy to bring us to a confrontation will fail," he wrote on Twitter.
Power was restored late Sunday in some areas of the capital Caracas, sparking enthusiastic cheers. But already twice so far, the restoration of electricity has been fleeting.
Guaido has called for more street protests on Monday to pressure Maduro to step down, following up on Saturday's rally.
"You have the right to go into the street, to protest, to demand, because this regime is letting Venezuelans die," he said Sunday, appealing to the armed forces "to stop covering for the dictator."
Electromagnetic attack?
Maduro blames "imperialism" for the country's accumulating woes, and claims the power outage was caused by an electromagnetic attack on the Guri hydroelectric complex, which supplies 80 percent of Venezuela's electricity.
Guaido dismissed that explanation as "Hollywoodesque." Critics blame the government for failing to maintain the power grid, as did the Lima Group, a primarily Latin American bloc.
For ordinary Venezuelans, the blackout - the longest in recent memory - has piled misery upon an already agonizing day-to-day struggle to survive in a country now in economic freefall.
"Every day is worse," Edward Cazano, a 20-year-old who lives with his mother and three brothers in a poor Caracas neighborhood called Pinto Salinas, said.
"We have the worst services in the world: no light, no water, sometimes no gas."
