The huge blaze, which broke out Saturday afternoon at Islam Qala port 120 kilometres (75 miles) from the western city of Herat, has largely been extinguished and an investigation has been launched to probe its cause.
"We were told that 100 or 200 tankers have been destroyed, but this number could be higher. We need more time to find out the extent of the damage," Jailani Farhad, the spokesman for the governor of Herat province said after visiting the scene.
Around 20 people injured in the fire have been taken to hospital, he added.
Videos posted on social media show towering flames and huge clouds of thick black smoke billowing into the sky.
The finance ministry said initial reports were that the fire started in a tanker before quickly spreading, causing "heavy financial losses", including of fuel, tankers and customs facilities.
A delegation has been despatched from the capital Kabul to investigate the blaze, the ministry added.
Younus Qazi Zada, the head of the Herat Chamber of Commerce, on Saturday said initial estimates were of "millions of dollars of losses".
Large parts of Herat province were without power on Sunday.
Islam Qala is one of the major ports in Afghanistan, through which most official trade with Iran is conducted.
Afghanistan has received waivers from Washington allowing it to import oil and gas from Iran despite US sanctions.
Iran foreign ministry spokesman Saeed Khatibzadeh said the border "was held open for trucks, cars and people running from the fire" towards Iran.
Afghan authorities called on Iran for help after saying it did not have the required resources to tackle the blaze alone.
Fire services from both countries were at the scene extinguishing small fires that still remain, Farhad said.
He added that Taliban insurgents attacked a nearby security post shortly after the blaze broke out.
Security forces have been deployed around the port to prevent any looting.
Afghanistan has been hit by a surge in violence despite peace talks that started in September between the Taliban and the Afghan government, which have so far failed to achieve a breakthrough.
The rise in violence has led US President Joe Biden's administration to launch a review of a deal signed between Washington and the Taliban last year that paved the way for the withdrawal of all American troops in the coming months.
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