Heartbreaking footage shows the mother screaming: "I'm not going to see my baby. I lost my baby. Why me? Where's my baby?"
The ship contacted rescue vessel Sea-Watch, who refused to take the bodies and the survivors on board without Italy's guarantee of safe harbor.
1,763 people drowned attempting to immigrate to Europe through the Mediterranean in 2017.
The rescued migrants from Nigeria, Ethiopia, Eritrea and Bangladesh were taken to a Sicilian port for questioning.
Friends and journalists have claimed that an Eritrean refugee has been arrested in a case of mistaken identity.
Mered Medhanie is believed to have smuggled thousands of people from Africa into Europe.
About 154,000 refugees crossed the Mediterranean from Libya into Europe in 2015.
The cold winter months have not stopped refugees and migrants from attempting the journey.
German, Italian and NGO boats rescued the migrants in 13 separate incidents.
Greece has overtaken Italy as the main entry point for those seeking refuge or a better life in Europe.
UK prime minister David Cameron will attempt to set out his intentions to renegotiate the UK's terms of its EU membership.
The influx of refugees has led to tensions in some regions of Germany and, occasionally, attacks by suspected neo-Nazis.
More than 5,000 migrants trying to reach Europe have been saved from boats in distress since Friday.
More people have drowned in the Mediterranean this year than in the Titanic disaster.
900 people drowned crossing the Mediterranean last week as EU leaders step up efforts to destroy traffickers' vessels.
EU leaders agree to triple naval search mission in Mediterranean following drowning of 900 people in past week.
Even as more migrants are crossing, the sea route from war-torn Africa is getting more deadly.