The ship was heading from Equatorial Guinea to Malta when it sank seven miles off the coast of the southern city of Gabes on Friday. The Tunisian Navy rescued all seven crew members after a distress call.
Officials said the tanker was carrying between 750 and 1,000 tons of fuel.
The Ministry of Defense did not name the countries that offered assistance, but local media said that Italy was expected to send a naval vessel specialized in dealing with marine disasters.
A specialized marine diving team began working around the ship to check for any oil leaks.
“The situation is reassuring and under control, and no gas oil leakage from the sinking ship’s tank has been recorded so far,” said Rabih Majidi, Minister of Transport.
The next stage, he said, is “delicate and delicate” as the ship must be taken out of the water without allowing it to leak.
On Saturday, the Tunisian authorities opened an investigation into the drowning accident, which the Ministry of Environment said was caused by bad weather.
“Tunisia will determine the losses later and will demand compensation,” Environment Minister Leila Shekaoui said.
The ministry said that barriers will be put in place to limit the spread of fuel.
The coast of Gabes has suffered from significant pollution for years, with environmental organizations saying that industrial facilities in the area dump waste directly into the sea.