Borrell was speaking after an emergency video conference of EU foreign ministers called to discuss the repercussions of the attack.
"Some member states proposed ... adopting an expansion of restrictive measures against Iran," Borrell told reporters.
"I will send to the External Action Service the request to start the necessary work related to these sanctions," he added.
Borrell said the proposal would expand a sanctions regime that seeks to curb the supply of Iranian drones to Russia so that it would also include the provision of missiles and could also cover deliveries to proxies in the Middle East.
Germany, France and several other EU members have publicly backed such a proposal.
Borrell said he supported the proposal and diplomats would work on it in the coming days so ministers could discuss it again at a meeting in Luxembourg on Monday.
(Reporting by Andrew Gray; Editing by Benoit Van Overstraeten)
