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Gen. Hossein Salami, deputy head of the Guard, said in remarks broadcast on state television that the violation of Iran's airspace by the US drone was a "hostile act" and warned of a "bigger" response. He did not elaborate on what Teheran might do.
"No-one returns the symbol of aggression to the party that sought secret and vital intelligence related to the national security of a country," Salami said.
Iranian television broadcast video on Friday of Iranian military officials inspecting what it identified as the RQ-170 Sentinel drone.
Iranian state media have said the unmanned spy aircraft was detected over the eastern town of Kashmar, 225km from the border with Afghanistan. US officials have acknowledged losing the drone.
Salami called its capture a victory for Iran and a defeat for the US in a complicated intelligence and technological battle.
"Iran is among the few countries that possesses the most modern technology in the field of pilotless drones. The technology gap between Iran and the US is not much," he said.
Officers in the Guard, Iran's most powerful military force, had previously claimed that the country's armed forces brought down the surveillance aircraft with an electronic ambush, causing minimum damage to the drone.
American officials have said that US intelligence assessments indicate that Iran neither shot the drone down, nor used electronic or cybertechnology to force it from the sky. They contend the drone malfunctioned. The officials had spoken anonymously in order to discuss the classified programme.
But Salami refused to provide more details of Iran's claim to have captured the CIA-operated aircraft.
"A party that wins in an intelligence battle doesn't reveal its methods. We can't elaborate on the methods we employed to intercept, control, discover and bring down the pilotless plane," he said.