Rigi said in a taped statement, made after he was taken into custody and broadcast on Iran's state-run English-language Press TV, that "they (the Americans) said they would cooperate with us and will give me military equipment.”
Jundallah said in its website posting: "Let the [Iranian] regime know that it will face a movement that is stronger and much more solid than ever before and one whose existence it has not been aware of.
"It will see what our believing heroes among our Baluch children can do to the occupiers, the aggressors and the unjust. The falsehood of the senior leaders of the regime will soon be exposed."
Jundallah says it is fighting Tehran's Shia government to secure rights for Sunni Baluchis who form a significant population in the eastern Sistan-Baluchestan province.
Tehran has long accused the group of being trained and equipped by American and British intelligence services as well as the Pakistanis in a bid to destabilise the government.
Washington denies the charges.