Terzi announced his resignation in Parliament, Italian news agency ANSA reported.
"I resign in contention with the decision to send the marines back to Italy. The misgivings I expressed had no effect on the decision taken," the 66-year-old told parliament.
The Italian marines accused of killing two fishermen off the Kerala coast last year had returned to New Delhi on March 22 after India gave an assurance that they will not face death penalty nor will they be arrested, bringing to an end a raging 11-day diplomatic row between the two countries.
The dramatic u-turn by the Italian government, which had earlier said the two marines would not be sent back, enabled the marines to meet the deadline set by the Supreme Court when it gave them permission to go for a month to vote in the elections there.
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Italy had said it was important to suspend the diplomatic assurance on sending back its marines as it needed to obtain assurances from India that the soldiers won't face death penalty.
External Affairs Minister Salman Khurshid had said that no deal has been worked out with Italy for bringing back the marines but the government had "clarified" to authorities in Rome that the case does not entitle death penalty.