Interior Minister Angelino Alfano urged more assistance from the European Union, a day after Prime Minister Matteo Renzi said: "Europe is leaving us on our own.
"It can't save governments and banks and then let mothers and children die," Renzi said in an interview on ReteQuattro television after Monday's shipwreck.
Mauro Casinghini, the director of rescue services in Italy for the Order of Malta, described one scene from the shipwreck as recounted to him by a medical worker on the scene, Antonella Godino.
A Somali woman, Amina, gripped a piece of wood floating in the water and held on to her four-month old baby with the other after the boat capsized and sank in international waters between Libya and Italy.
"The waves were lapping at her chin and she was barely holding her baby above the water," Casinghini cited Godino as saying.
"When we held the little baby, we were afraid his heartbeat would not come back. We dried him, wrapped him up in a thermal blanket and put him in the warmest place we could find - next to the engine room," she said.
Casinghini said there were around 250 people on board, most of them from Eritrea, Pakistan, Somalia and Syria.
Italian media cited coast guards as saying there may have been many more asylum-seekers - around 400 people - which would leave dozens still unaccounted for.
"We don't know how many were on board but the survivors told us hundreds," Giuseppe Cannarile, a coast guard, was quoted by the La Stampa daily as saying.
The Italian navy said in a statement that 206 survivors were rescued and 17 bodies had been recovered "so far", increasing a previous toll from Monday of 14 killed.
Merchant ships to the rescue
The navy said two warships, three coast guard and border patrol boats had taken part in the rescue, along with two merchant ships - the Vanuatu-flagged Kehoe Tide and the French ship Bourbon Arcadien.
"They reached the capsized ship as quickly as possible," the navy said, adding that two helicopters and two planes had also taken part in the rescue.
One of the Italian warships, the Grecale frigate, was headed for the port of Catania in Sicily with the survivors and the bodies of the victims on board.
Italian media said it was expected at 1600 GMT, later than previously thought due to poor weather.
The captain of the Grecale, Stefano Frumento, told La Repubblica: "When we arrived on the scene, 14 bodies had already been recovered" by the crews of commercial ships scrambled to the scene by the coast guard.
"Our men found three more we dragged aboard," he said.
La Repubblica said the migrant boat did not sink right away and rescuers managed to board it to evacuate people before it capsized at around 1100 GMT.
It said many victims were Eritrean and Somali teenagers.
"They managed to rescue dozens of people who were terrified below deck or gripping the handrail or in the water trying to stay afloat," the report said.
Prosecutors in Catania said they would be opening an investigation into the causes of the shipwreck and local officials were preparing places for the survivors.
The navy said its second warship, the Sirio, had gone on to rescue 295 migrants from another stricken boat.
Hundreds of migrants - many of them from Eritrea, Somalia and Syria - are landing on Italy's shores on an almost daily basis and the government has appealed for more assistance from the European Union.
The Italian navy launched a large-scale operation to rescue migrants and deter traffickers following two separate shipwreck tragedies in October 2013 in which more than 400 people drowned off Italy's shores.
The interior ministry said that 36,000 people have landed in Italy so far in 2014 compared to 42,925 people for the whole of 2013, 13,267 in 2012 and 63,000 in 2011 at the height of the Arab Spring revolutions.
La Repubblica said 700 migrants perished making the crossing in 2013, 102 in 2012 and 2,352 in 2011.