At least 33 people perished after the boat sank on Friday, a week after another shipwreck off Italy left at least 359 dead, prompting Malta to warn that the Mediterranean was becoming "a cemetery".
The boat, carrying up to 400 migrants, mostly Syrians, left the Libyan port of Zwara on Thursday, just 60 kilometres from the Tunisian border in chaotic conditions.
Some of the 206 known survivors said Libyan militiamen shot wildly at them, leaving several people dead and causing the vessel to take on water and sink.
Mohammed said he had paid USD 4,800 for the trip to seek a better life in Europe, crossing through Egypt to Libya.
"When we got on the boat, Libyan militia put their machine guns to our heads and demanded more money. I had USD 5,000 and they took this too," Mohammed said from a detention camp in Malta.
He said the Libyan gunmen followed them for four or five hours.
"Then they started shooting more bullets at the boat and they managed to puncture it. Lots of water started coming in. It was filling quite fast until we all ended up in the sea. I grabbed my daughter. She swallowed water but I managed to swim and we got onto a raft rescuers threw in the water," Mohammed said.
Citing survivors' accounts, the UN refugee agency spoke of several injured passengers, saying shots were fired "perhaps by militiamen who shot to kill".
He said he thought the attacks were related to a dispute between different groups of human traffickers.
"There was a furious fight, screaming on the radio and on the phone with someone who demanded that we return to land, but the captain did not stop."
The ANSA news agency said witnesses spoke of two people being killed.
Once they reached Malta, the Tunisian captain was arrested after being recognised by survivors, according to media reports.
"I lost practically all I had,"Ashur, a Syrian, said he and his family were fleeing the civil war in his home country. When the vessel capsized he managed to save his two-year-old daughter but lost his son and wife who was pregnant with twins.
