The Italian coastguard says it has also rescued about 500 people in the Mediterranean this weekend.
And with the flow of migrants into Europe showing no sign of slowing, Hungary is stepping up its military response.
The overcrowded migrant boat was carrying 37 people from Turkey's Bodrum coast on its way to the Greek island of Kos.
The 20 people rescued were on deck, wearing life jackets -- the victims were trapped in the cabin.
The Italian navy launched seven operations over the weekend to avoid similar tragedy.
On Sunday alone 245 migrants were rescued from two rubber boats - among them 51 women and five newborn babies.
Those lucky enough to already be on land know winter is coming.
The journey through Serbia, Croatia, Hungary - hopefully to Austria or Germany - is getting harder.
German volunteer Frieda, at the Serbia-Croatia border, says migrants are braving the cold and the wet with little more than disposable raincoats.
"Most of the people who are arriving are quite exhausted by the long journey and waiting. They have really long waiting times. But there's also great thankfulness and people are happy to receive some warm food and some clothes for their children."
In Hungary, with numbers topping 10,000 a day, the military is strengthening its presence at the border.
Their response is as if it's a siege, with vehicles and heavily armed soldiers escorting migrants to the Austrian border.
One migrant says it's like entering a military-governed country.
But aid worker Dorottya Retfalvi says small children already exposed to war shouldn't now have to face big men with big guns.
"While they are waiting we try to cheer them up with water or fruit or some sweets. If we really have to we give them a toy to help ease the tension."
In Austria, Burgenland Police spokesman Gerald Koller says they're overwhelmed, and yet more are expected.
"Yesterday 12,000 people arrived here in Nickelsdorf. In the night, 3,500 people arrived and then this morning a train with around 1,500 people. So we have a total of around 5,000 people here already."
With thousands more migrants also arriving in Vienna, Red Cross spokesman Thomas Wagner says with such numbers, it's hard to prepare for winter.
"It is difficult because we don't know how long it will go on for. That makes it difficult for us but of course we are preparing for the cold months. We are thinking about moving the medical treatment to a hall and we are trying to organise large tents with heating. The plans are starting in the background already for the colder months."
But the winter cold is unlikely to stop or slow the flow of desperate and determined migrants.
In just four hours, another 4,000 arrived in mainland Greece from Lesbos island.
A world away at the United Nations, US President Barack Obama has called on wealthy nations to act.
"Women and children have been forced from their homes, many by conflicts in the Middle East and Africa. These are humanitarian crises and refugees that we cannot ignore and we have to deliver the urgent aid that is needed right now. And those countries that can, must do more to accommodate refugees, recognising that these children are just like ours. But our efforts must be matched by the hard work of diplomacy and reconciliation to end conflicts that so often tear societies apart."
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