At least 40 people have been confirmed dead, says the local governor to state TV. Many of the injured have been taken to Tehran for care.
According to the Iranian news agency Isna, which refers to local authorities, over 1,200 people have been injured.
The fire after Saturday's giant explosion is said to be under control but not extinguished. Helicopters and planes are said to have water-bombed the area during the night, but images on state TV show that black smoke is still rising from the Shahid Rajaee port area. The extinguishing work is being hampered by strong winds and there are fears that the flames will spread.
The President on site
President Masoud Pezeshkian arrived at the area on Sunday and expressed appreciation for the rescue service's efforts.
We will try to take care of the families who have lost their loved ones and we will definitely take care of the people who have been injured, he says.
Interior Minister Eskandar Momeni is also on site in Bandar Abbas to follow the efforts and investigation of the incident, writes state-owned Irna.
Schools in the province of Hormozgan are closed on Sunday so that the authorities can focus on extinguishing and rescue work.
The port of Bandar Abbas is described by Irna as the country's largest for container ships, 80 percent of Iran's container transport is handled in the port.
A local mourning period of three days has been declared.
Cause unknown
The cause of the explosion is not known. A representative of the port's customs office says that the fire started in a warehouse where hazardous chemicals were stored, according to reports in state media.
Rumors are circulating that port officials in March received rocket fuel from China, according to the private security company Ambrey. Iran has not confirmed the reports. The Defense Department claims on Sunday that no military equipment was present at the site.