“We are so tired of everything happening here,” said Leidy Medina, 31, a nurse who said she walked two hours to reach the demonstration. On top of all the other effects of a severe economic crisis, she noted, the country had been paralyzed since Thursday by a blackout. “So many kids are dying in hospitals” without electricity, she said.

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Although power returned to many areas Saturday morning, it soon failed again in much of the country. On Saturday, 96 percent of the nation’s telecommunications network was knocked off­line, according to NetBlocks, a U.S.-based Internet freedom group.

Saturday’s demonstration against President Nicolás Maduro’s administration was unusual in that it took place near the Miraflores presidential palace, in a neighborhood once considered pro-government. Police clutching ­anti-riot shields closed a street about a mile from the site in the early afternoon, blocking thousands of protesters from arriving. The demonstrators responded with pro-Guaidó chants and a recitation of the Lord’s Prayer. After a tense half an hour, officers let them pass.

“It was really difficult to get here, because there was no metro,” said Jorge Araiy, 22, an employee of the private TV channel Venevision. He said he walked four hours and took a bus before hitting the police barricade. But he expressed relief that he eventually got through. “In the past, the police didn’t let us go to rallies,” he said.

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Opposition activists said three Guaidó supporters were detained early Saturday as they tried to set up a stage for his rally. Calls to government spokespeople for comment were not returned.

Maduro’s government has largely ignored Guaidó since he declared himself president in late January, apparently hoping the opposition movement would exhaust itself, as previous efforts have. Maduro has maintained the backing of the powerful armed forces and controls paramilitary groups known as “colectivos.”

On Saturday, Maduro appeared at a “day of anti-imperialism rally” in central Caracas, saying he was “facing my responsibilities as the elected and legitimate president of Venezuela.” It was his first public appearance since the start of the blackouts — the worst in living memory in this oil-rich country. He spoke in a sector of the city that did not have power.

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Maduro has alleged that the U.S. government was behind the outage, a claim that Washington denies. He said that 70 percent of the nation’s electricity had been restored on Saturday morning “when we received another attack” on the system.

Electrical experts said the blackout was more likely a result of corruption, a lack of maintenance, the exodus of skilled workers and the soaring cost of imported parts when paid with Venezuela’s devalued currency.

The power failure has dealt a further blow to a country already suffering from hyperinflation and shortages of food and medicine. Demonstrators said Saturday that the blackout was the last straw after months of privation.

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“It ruined the little food we had,” said Marisol Cartagena, 54, a fruit seller, describing how she had to toss out some fish after it went bad in her refrigerator during a power outage.

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Guaidó, the National Assembly president, argues that he is the legitimate president because Maduro won reelection last year in a contest marred by fraud, making the office technically empty.