Jundallah has threatened to execute a kidnapped Iranian nuclear plant worker and denied the 11 men hanged in Iran this week were members of the Sunni group, its spokesman told a Saudi daily on Wednesday.
Jundallah spokesman Abdel Raouf Rigi is quoted Wednesday by the London-based Asharq Al-Awsat daily as saying the hostage would be killed "very soon."
"We will execute this man after the Iranian authorities did not respond to our demands," Abdulrauf Rigi, the group's spokesman and brother of its leader Abdolmalek Rigi who was hanged in June, told the paper.
Jundallah has demanded that Tehran free more than 200 Sunni and Baluch political prisoners and members of the Sunni group it says are being held in Iranian jails.
The shadowy militant group has claimed the kidnapping of 39-year-old Amir Hossein Shirani, an "employee at a nuclear plant" in Iran's central province of Isfahan.
Shirani is a welder and driver for a nuclear organization, according to Iranian authorities.
Rigi also told Asharq Al-Awsat that the 11 militants hanged on Monday in Iran following last week's devastating suicide bombing of a Shiite mourning procession did not belong to his group.
"Iran is lying as usual. Those (hanged) are not members of the organization. They have tribal links to some resistance fighters, but they had nothing to do with our recent operations in Iran," he said.
The newspaper said Rigi was speaking on the telephone from "somewhere inside the Baluchestan mountains."
Jundallah (Army of God) has claimed several deadly attacks in Sistan-Baluchestan, of which Zahedan is the capital and which borders Afghanistan and Pakistan.
On December 15, a suicide bombing in the city of Chabahar killed 39 people and wounded dozens. Jundallah said its attack was to avenge the hanging of its leader Rigi.
The group says it is fighting for the rights of the ethnic Sunni Baluchis who make up a significant population of predominantly Shiite Iran's Sistan-Baluchestan province.
The group has been waging a deadly insurgency in southeast Iran for almost a decade. Iranian officials charge that the group receives support from the intelligence services of the United States, Britain and Pakistan.