"Their grossly unfair trial was marred by allegations of torture and forced confessions," Amnesty said in a statement Monday.
Behrouz Ehsani, 69, and Mehdi Hassani, 48, had their death sentences upheld by Iran's Supreme Court earlier this month.
Mostafa Nili, a lawyer representing Ehsani, said on Monday that the Supreme Court had ordered a temporary halt to Ensani's execution.
"Today, along with my esteemed colleague Mr. Babak Paknia, we visited the Supreme Court branch. We learned that the branch, in accordance with the law, issued an order yesterday to halt the execution of Mr. Behrouz Ehsani Aslamlou's sentence. The sentence will not be carried out until the review of the retrial request is completed," Nili wrote in a post on X.
No such announcement has been made regarding Hassani, leaving his fate uncertain.