At least 43 people were missing off the southeastern coast of Tunisia after a boat carrying more than 120 migrants sank, the Tunisian Red Crescent said on Saturday.

"Eighty-four migrants were rescued and 43 others disappeared after a boat carrying 127 migrants sank off the coast of Zarzis" on Friday night, Mongi Slim of the Red Crescent told AFP.

The vessel had set off from Libya's coast, he added, citing the accounts of survivors.

The Tunisian navy rescued "84 illegal migrants of various nationalities" including from Bangladesh, Chad, Egypt, Eritrea and Sudan, the defence ministry said.

The survivors picked up off Zarzis were aged between three and 40, the ministry said, without giving any number for those missing.

It said that the boat had departed the port of Zuwara, in northwestern Libya during the night between Monday and Tuesday.