The five-day old siblings had been born prematurely during their mother’s journey to Europe and were found packed on a dangerously overcrowded boat with hundreds of other migrants.
Doctors Without Borders (MSF) said one of the twins was “desperately ill” and that both infants were evacuated to shore with their mother for emergency care.
Antonia Zemp, the medical team leader on board the charity’s rescue boat, said the woman had been travelling alone.
“One of the boys was not well,” she added. “He was vomiting, had hypothermia and non-reactive.
“Our medical team decided to request an evacuation due to the fact that his health was so fragile that he would not have survived the long journey to Italy in our boat.”
They were among at least 6,500 migrants rescued while attempting the deadly crossing to Italy on Monday, in a concerning spike for humanitarian groups attempting to prevent disasters at sea.
MSF assisted the rescue of 3,000 people off the Libyan coast, taking 435 men women and children on to its Dignity I vessel and distributing 700 life jackets to those drifting at sea.
Those rescued including 13 children under the age of five, 110 minors – mostly unaccompanied teenagers – and 82 women.
Aid agencies found asylum seekers suffering from hypothermia, fevers, dehydration and skin diseases after rescuing them from overloaded rubber dinghies and wooden fishing boats.
“This is one of the largest numbers of people we have assisted in any single day since our search and rescue operations began over a year ago,” said Nicholas Papachrysostomou, the field co-ordinator for Dignity I.
“This unbelievable number speaks to the desperation people are facing in their countries that pushes them to risk their lives to seek safety and protection in Europe….the EU’s response to the crisis at and within its borders has failed to address the urgent humanitarian and protection needs of refugees and migrants.”
The operation came just weeks after a rescue vessel was boarded by armed men who shot at aid workers off the coast of Libya.
MSF is joining other humanitarian groups calling for safe and legal routes to Europe to be opened following the deaths of more than 3,000 migrants in the Mediterranean so far this year
The vast majority of asylum seekers are currently arriving on the Central Mediterranean route between Libya and Italy, since efforts to stop crossings over the Aegean Sea with the EU-Turkey deal.
But more than 460 migrants and refugees arrived on Greek islands on Tuesday alone - the highest figure in several weeks.
Most entered through the Aegean islands of Lesbos and Kos, where asylum seekers are detained until their applications are decided – being deported to Turkey if they are unsuccessful.
More than 160,000 migrants have arrived by sea in Greece so far this year, mostly Syrians, Afghans and Iraqis, and 105,000 in Italy, where the majority of asylum seekers come from Nigeria, Eritrea, Sudan and other African nations.
A record high of around 9,000 refugees hoping to travel to the UK are living at “The Jungle” camp in Calais, which has been the subject of discussions between Home Secretary Amber Rudd and her French counterpart Bernard Cazeneuve.
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