One of those on board called the BBC Somali Service on Thursday night to say that the boat's generator had failed and their water supplies had run out.
He said they had left the Libyan capital, Tripoli, hoping to reach the Italian coast.
The migrants were rescued in a joint Libyan and Italian operation.
Earlier this month, 54 people died of dehydration while trying to sail from Libya to Italy in an inflatable boat.
Relatives of those aboard the boat confirmed to the BBC that they had been found.
In his call to the BBC's Somalia Service on Thursday, passenger Abdi Amin Omar said: "We are in a terrible situation."
"We have been floating out to sea now for four days and we don't know where we are heading or exactly where we are now. All we can see is the dark sea," he told one of the BBC producers who phoned him back.
"We desperately need help. Some of us are badly injured and there are several vulnerable pregnant women."
Mr Omar said they had tried to contact the coastguard and were given another number to call, but that there was no answer on that number.