It was not immediately clear what caused the boat to sink, but vessels leaving the North African coast for Europe are often heavily overloaded makeshift crafts, departing at night even in rough weather to avoid detection by the coastguard.
Tunisian rescuers were bringing the survivors to the port of Zarzis, some 100 kilometres (70 miles) northwest of Zuwara.
Departures from Libya, a key gateway for Europe-bound migrants, have increased since the start of the year.
On Monday, the Tunisian navy said it had rescued more than 100 migrants, mainly from Bangladesh and Sudan, whose boat was “on the verge of sinking”
There were 11,000 departures between January and April, 73 per cent more than the same period last year, due in particular to the “deterioration” of the situation for foreigners in the country, according to the UN refugee agency, UNHCR.
Neighbouring Tunisia regularly provides assistance to migrants in difficulty in the central Mediterranean, one of the deadliest migration routes, according to the United Nations.
Oil-rich Libya has been torn by conflict since the toppling and killing of dictator Moamer Kadhafi in 2011.
But in October, rival groups signed a truce, setting in motion an UN-led process that saw a new transitional government installed.
“Despite the improvement in the political situation, there are more and more cases of (migrant) detentions, and neither UNHCR nor the IOM have had access to the centres since March,” Vincent Cochetel, UNHCR’s special envoy in the region, told AFP.
He said refugee evacuation flights from Libya towards transit centres in Niger or Rwanda had been “blocked since February due to Libyan bureaucracy”, pushing some migrants to take to the sea.
The UN says more than 700 people have died trying to cross the Mediterranean this year, compared to 1,400 for all of last year.
On Monday, the Tunisian navy said it had rescued more than 100 migrants, mainly from Bangladesh and Sudan, whose boat was “on the verge of sinking”.
That boat reportedly also departed Sunday from Zuwara.
Several boats were also stopped by Libyan coastguards and brought back to shore overnight Sunday to Monday.
“Two days ago about 680 migrants were intercepted at sea and returned to Libya,” Di Giacomo said.
‘Human rights violations’
“Almost 9,000 people have been intercepted at sea and returned to Libya in 2021 so far,” he added.
Safa Msehli, IOM spokeswoman for the Geneva-based UN agency, said that support for search and rescue teams should depend on “no one being arbitrarily detained or subjected to human rights violations”.
The European Union has for several years supported Libyan forces to try to stem migration, despite often grim conditions in detention centres in Libya.
International agencies have repeatedly denounced the return to Libya of migrants intercepted at sea.
In Lisbon last week, Tunisia’s prime minister Hichem Mechichi repeated his country’s opposition to setting up migrant reception centres on Tunisian soil, amid attempts to find safe places for asylum seekers.
Italy’s interior minister is expected in Tunisia later this week, together with the EU commissioner for home affairs, Ylva Johansson, to discuss assistance and repatriations.