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.