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The Iranian foreign ministry issued a statement, quoted by the state IRNA news agency, condemning the blasts and offering condolences to the victims' families.
The statement added: "Doubtless instability and threats to Syria's national security, which is what its enemies are after, will not only pose a threat to Syrians but also other nations in the region."
Friday's attacks in Damascus hit two bases belonging to the Syrian security service, which has been cracking down on pro-democracy protesters since March.