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Supporters of the mayor of Caracas, Antonio Ledezma, demanded his release on Thursday.CreditAriana Cubillos/Associated Press 
CARACAS, Venezuela — The abrupt arrest of the mayor of Caracas on accusations that he had plotted an American-backed overthrow of the government threatened to plunge Venezuela into new political convulsions on Friday, as his supporters rallied in the capital and pockets of protest erupted elsewhere.
The arrest of the mayor, Antonio Ledezma, on Thursday evening by intelligence agents who fired weapons in the air, was viewed by the opposition as the kidnapping of a political rival to President Nicolás Maduro.
Mr. Ledezma’s backers called it another assault on democracy in Venezuela, the oil-endowed nation that has been reeling from a severe economic decline under the watch of an increasingly unpopular president.
Many opposition figures said Mr. Maduro, desperate to divert attention from Venezuela’s internal ills and his own disapproval ratings, concocted Mr. Ledezma’s arrest.
Mr. Maduro, the protégé of Venezuela’s longtime leader Hugo Chávez, often castigates the United States, accusing it of trying to topple his government. He promised, in a nearly three-hour speech soon after the mayor’s arrest, to release evidence to demonstrate what he called the secret American plot to topple him.
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National police officers stood guard in Caracas on Thursday outside Venezuela's intelligence service.CreditMiguel Gutierrez/European Pressphoto Agency 
“Every fascist has his day,” Mr. Maduro said.
“I have heard them saying that this is a lie, this is a show,” he said, speaking of his political adversaries. “Because the United States gave the order, you have to mock the accusation, it must be trivialized. This is serious.”
Mr. Ledezma’s lawyer, Omar Estacio, met with his client soon after the arrest. “He’s content, in a happy state of mind and not scared of anything,” Mr. Estacio said, adding that Mr. Ledezma, 59, had sensed that something was awry.
“He started to be followed around two weeks ago by cyclists, black cars, et cetera,” the lawyer said. “He had a feeling, therefore, that something like this would happen.”
Mr. Estacio and other witnesses described the method of arrest as disproportionately severe. They said Mr. Ledezma had been working calmly in his office when a dozen armed officials burst in, fired into the air and dragged the mayor away to the intelligence agency’s headquarters.
Mr. Maduro confirmed that the mayor would be dealt with by Venezuela’s judicial system on what he described as charges committed against the country’s “peace, security and constitution.”
A hard-line opposition figure and ally of Mr. Ledezma, María Corina Machado, was charged in December with plotting to assassinate Mr. Maduro.
“If anyone in Venezuela knows about coup-plotting, it’s Mr. Maduro and those in power right now,” said Ms. Machado, referring to a failed coup attempt by Mr. Chávez in February 1992, which the government here continues to celebrate.
The United States has repeatedly denied Mr. Maduro’s charges. “These latest accusations, like all the previous such accusations, are baseless,” the State Department said in a statement.
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Mr. Ledezma was accused by President Nicolás Maduro of plotting with the United States to overthrow him. The State Department issued a statement saying, “Venezuela’s problems cannot be solved by criminalizing dissent.”CreditCarlos Garcia Rawlins/Reuters 
“The United States is not promoting unrest in Venezuela, nor are we attempting to undermine Venezuela’s economy or its government,” the statement read. “Venezuela’s problems cannot be solved by criminalizing dissent.”
Venezuela is the fourth-largest provider of crude oil to the United States.
Many government critics suggested that Mr. Ledezma’s arrest was a means to silence the opposition before legislative elections later this year. The opposition is able to call for a recall referendum in 2016.
Gladys Ramírez, a lawyer who attended a rally Friday against Mr. Ledezma’s arrest, said he had been detained because he was the type of leader who could push the government out of power. “This government has lost all perspective,” she said. “This isn’t democracy. We’re suffering a dictatorship.”
María Martínez, 68, a retiree, said the government was trying to put a stranglehold on the opposition. “The opposition has been kidnapped, and so the people have been kidnapped,” she said. “We’ve all been kidnapped. I don’t know if this is a dictatorship, communism or what. But it’s not a democracy.”
Mr. Ledezma’s arrest came nearly a year after the detention of Leopoldo López, a popular hard-line opposition figure who remains in jail on charges of inciting nationwide unrest.
The collapse in the international price of oil, from which Venezuela derives nearly all of its foreign income, is an important reason for its economic ills. Annual inflation was at 69 percent in 2014, and the country’s currency has fallen more than 50 percent in value against the dollar on the black market in the last year. Shortages leave supermarket shelves across the country nearly empty and lines stretching sometimes into the thousands.
“The government is showing force and generating fear,” said Luis Vicente León, director of Datanálisis, a polling firm, which has calculated Mr. Maduro’s approval ratings in the low 20 percent.
Mr. Maduro’s unpopularity, combined with the troubled economy, is raising fears of major unrest like that of early last year, when tens of thousands took to the streets and pitted themselves against the authorities in battles involving Molotov cocktails, rubber bullets and tear gas.
“All us Venezuelans that express views differing from those of Nicolás Maduro have our days numbered,” said David Smolansky, the mayor of the nearby municipality of El Hatillo and a member of the opposition party. “The question is when the guillotine falls.”