Coastguards in Falmouth co-ordinated a rescue operation after an Ethiopian in the UK took a call from the inflatable boat from his half-brother on board.
The Italian authorities sent an aircraft which spotted the boat.
Coastguards said the boat was taken to a Sicilian island but could not confirm the condition of the 59 passengers.
The original call said there were 15 women, seven children and 37 men on board, and had been without water or supplies for three days.
"This is a truly awful episode of human trafficking"
Alex Berhanu, from London, was called by his half-brother who said they were trying to reach Europe and were told they were in Italian waters before being left in the leaking inflatable off the coast of Libya.
He said: "I could hear them screaming and crying, it was ear piercing. I have never heard anything like it."
Falmouth Coastguards sent a distress call to ships in the area and contacted the Italian and Maltese authorities as well as the British Embassy in Tripoli.
A Tunisian ship first responded to a call for help but, despite a search, found nothing.
The Italian aircraft saw several other boats, which were believed to contain another 200 migrants but had not sent any distress calls.
Simon Rabett, rescue centre co-ordination manager at the Maritime and Coastguard Agency (MCA) said: "This is a truly awful episode of human trafficking."
The Falmouth team used an "enhanced group call" to alert vessels in the specific search area. This enables them to pinpoint any area of sea and then contact vessels within it.
^ Back to top | BBC Sport Home | BBC Homepage | Contact us | Help | ©
~RS~q~RS~~RS~z~RS~49~RS~)