The Spanish interior ministry and civil guard said in a joint statement they had arrested four people from the group, which is also accused of sharing technological information through a complex business network, including engineering projects, which may be used to build missiles.
The bust came as chief negotiators prepared for another round of talks in Vienna on Tehran's nuclear program, part of efforts to reach an agreement by late July on resolving a decade-old dispute that has stirred fears of a Middle East war.
The four suspects - three Spaniards and one Iranian - were arrested in Barcelona, Tarragona and Palma de Mallorca, the Spanish statement said.
The operation, dubbed "Terracota", began last year after police registered the acquisition of two pieces of machinery from a British defense company.
"Officials confirm that the machinery was introduced illegally into Spain in an attempt to hide its real destination, and with the goal of waiting for the right moment to send to Iran," the statement said.
The dual-purpose machinery, which could be employed for both military and civilian purposes, may be used to manufacture missile casing as well as parts which could be included in gas centrifuges for uranium enrichment, it said.
Western powers want Iran to significantly scale back its nuclear activities in order to deny it any capability of quickly diverting them to the production of a nuclear bomb, if it decided to "weaponize" its enrichment of uranium.
Iran says its enrichment program is a peaceful bid to generate electricity and denies having any nuclear bomb designs.
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