If the death toll is confirmed, it will bring to 1,500 the total number of people who died this year seeking to reach Europe - a swelling exodus that prompted Europe to downsize its seek and rescue border protection program in a bid to deter them. International aid groups strongly criticized the decision.
After news of Sunday's disaster several government leaders called for emergency talks and EU foreign policy chief Federica Mogherini said foreign ministers would discuss the immigration crisis at a meeting in Luxembourg on Monday. European Council President Donald Tusk said he was considering calling a special meeting of EU leaders, a summit that Renzi had called for earlier.
Meanwhile Italian and foreign ships and helicopters worked into the night to find possible survivors. So far 28 people have been rescued and 24 bodies recovered, Italian authorities said.
The 20 meter-long vessel sank 70 miles from the Libyan coast, south of the southern Italian island of Lampedusa, as a large merchant ship approached it. A survivor told the United Nations' refugee agency UNHCR that 700 people on board, hopeful the ship would save them, moved to one side, toppling the boat.
Italian Prime Minister Matteo Renzi said details were still "nebulous" and that he couldn't estimate the total death count.
French President Francois Hollande said the EU had to do more, telling Canal+ television that rescue and disaster prevention efforts needed "more boats, more over flights and a much more intense battle against people trafficking."
"More EU countries must take responsibility for the refugee situation," said Sweden's Minister for Justice and migration Morgan Johansson. He called for an expansion of the EU's Triton border protection program, the scheme that recently replaced a broader search and rescue mission run by Italy.
The Italian "Mare Nostrum" was canceled last year because of the cost and because some politicians said it encouraged migrants to depart by raising their hopes of being rescued.
"It was an illusion to think that cutting off Mare Nostrum would prevent people from attempting this dangerous voyage," said the German government's representative for migration, refugees and integration, Aydan Ozoguz.
Yet Renzi warned that resolving the crisis was not only a matter of search and rescue at sea. He said a concerted international effort was needed to locate and stop people traffickers, many of whom have flourished during the chaos among warring clans in Libya.
"We mustn't leave the migrants at the mercy of criminals who traffic human beings," Renzi told the news conference. "We are asking not to be left alone."
"LOOKING FOR A BETTER LIFE"
Carlotta Sami, a UNHCR spokeswoman, said initial information about the capsized boat came from one of the survivors who spoke English.
This survivor "said that at least 700 people, if not more, were on board. The boat capsized because people moved to one side when another vessel that they hoped would rescue them approached," Sami said.
She later added that "several sources confirm the death of at least 700 people."
Renzi said Italian and foreign navy and coast guard vessels, patrol boats and merchant ships, as well as helicopters, were involved in the search-and-rescue operation, which was being coordinated by the Italian coast guard in Rome.
Maltese Home Affairs Minister Carmelo Abela said the survivors and the corpses were on an Italian naval vessel coming to Malta, from where the survivors would continue on to Italy.
Pope Francis, who has spoken out repeatedly on the migrant crisis, repeated his call for quick and decisive action from the international community.
"They are men and women like us, our brothers seeking a better life, starving, persecuted, wounded, exploited, victims of war. They were looking for a better life, they were looking for happiness," he told tens of thousands of people in St. Peter's Square for his Sunday noon address.
Aid groups have called for the opening of a "humanitarian corridor" to ensure the safety of the migrants but in Italy there were also calls to stop the boats from leaving and even to destroy them.
The leader of the anti-immigrant Northern League party, Matteo Salvini, called for an immediate naval blockade of the coast of Libya while Daniela Santanche, a prominent member of Silvio Berlusconi's Forza Italia party said Italy's navy must "sink all the boats."
Libya's lawless state, following the toppling of former leader Muammar Gaddafi in 2011, has left criminal gangs of migrant smugglers free to send a stream of boats carrying desperate migrants from Africa and the Middle East.
Around 20,000 migrants have reached the Italian coast this year, the International Organisation for Migration (IOM) estimates. That is fewer than in the first four months of last year, but the number of deaths has risen almost nine-fold.
Last week, around 400 migrants were reported to have died attempting to reach Italy from Libya when their boat capsized.
"A tragedy is unfolding in the Mediterranean, and if the EU and the world continue to close their eyes, it will be judged in the harshest terms as it was judged in the past when it closed its eyes to genocides when the comfortable did nothing," Maltese Prime Minister Joseph Muscat said.