The two were arrested in Haiti last week and taken by the US Drug Enforcement Administration to New York and charged with drug trafficking.
Diosdado Cabello said the arrests were “irregular” and had been carried out to damage the governing party ahead of legislative elections on December 6.
US-Venezuelan ties have been fraught.
The US and Venezuela have not exchanged ambassadors since 2012 and Venezuela regularly accuses the US of trying to destabilize the Latin American country.
Diosdado Cabello, a powerful figure in the governing United Socialist Party (PSUV), was the first official to speak out about the arrest of the two men on November 10.
In an interview with Venezuelan TV, Diosdado Cabello said that he did not consider it an arrest.
“A plane went to Haiti with six people and they kidnapped two,” he said referring to the fact that the four other people on board had not been charged.
“It’s the DEA’s normal procedure to kidnap lots of people,” he alleged.
The aim of the arrests, Diosdado Cabello added, was “to hurt the Bolivarian revolution” in the midst of an election.
Some polls suggest that the governing coalition could lose its majority in the National Assembly for the first time in 16 years on December 6.
Efrain Antonio Campo Flores, 29, and Franqui Flores de Freitas, 30, were charged with one count of drug trafficking on November 12.
The two are nephews of first lady Cilia Flores and travelled on diplomatic passports.
Diosdado Cabello said they had acted independently: “These are grown men who can do what they want in life.”
Their indictment accuses the men of conspiring to import “five kilograms [11 lb] and more of mixtures and substances containing a detectable amount of cocaine” to the US.
A US law enforcement source had told Reuters that the two men had allegedly planned to smuggle a much larger amount, 800kg, to the US.
Lawyers for Efrain Antonio Campo Flores and Franqui Flores de Freitas said they would plead not guilty at their next court appearance.
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