The ship was en route from Equatorial Guinea to Malta when it sank 11 kilometers off the coast of the southern city of Gabes on Friday. The Tunisian Navy has rescued all seven crew members after a distress call.
It was carrying between 750 and 1,000 tons of fuel, officials said.
The defense ministry did not name the countries that had offered to help, but local media said Italy was expected to send a naval vessel specializing in dealing with disasters at sea.
A specialized sea diving team has started working around the ship to check for oil leakage.
“The situation is reassuring and under control, and so far there has been no leakage of gas oil from the tank of the sinking ship,” said Transport Minister Rabie Majidi.
He said the next stage was “delicate and sensitive” as the ship must be lifted out of the water without any leakage.
On Saturday, Tunisian authorities opened an investigation into the sinking, which the environment ministry said was caused by bad weather.
“Tunisia will later determine the losses and demand compensation,” said Laila Chikaoui, the environment minister.
The ministry said barriers would be erected to limit the spread of the fuel.
The Gabes coast has suffered from severe pollution for years, with environmental groups saying industrial plants in the area dump waste directly into the sea.