The two planes were allegedly smuggling drugs from Central America and refused to respond to military orders, the BBC reported Monday.
The first plane was shot down early Saturday after "all other means of persuasion had been exhausted," said Gen. Vladimir Padrino Lopez, the head of the country's Strategic Operational Center.
"This was the first plane shot mid-air in the country since the approval of the Law and Control Regulation for the Integral Defense of the National Airspace [earlier in the month], following the orders of our commander-in-chief, President Nicolas Maduro," Padrino said.
The second plane was shot down as it tried to land on an illegal airstrip in the jungle, the BBC said.
"These are drug-trafficking mafias which intend to use our country as a platform for drug distribution, trespassing our airspace," said Alejandro Keleris Bucarito, the head of the National Anti-Drugs Agency.
There was no immediate word on injuries or deaths.
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