Mohammad Amin Amani, head of the Ports and Maritime Department in the city of Jask, said on Wednesday that the rescue operation took place 30 miles (about 50 km) off the coast of the port city earlier in the day.
Relief and rescue vessels were dispatched to the area when the Cook Islands-flagged was sinking due to a storm, he further said.
Amani added that 21 crew members were rescued, and five of them received medical care provided by Jask emergency services.
Those receiving the medical care are now in good physical condition, the official said.