Giuliano Amato, the interior minister, said in a statement on Saturday that "what happened today is not only a tragedy but nothing less than a crime.
"And if we don't manage to punish crimes, they repeat themselves and tragedies repeat themselves too."
The boat, a 10-metre-long wooden vessel believed to have left from Libya, sank at about 3:30am (0030 GMT) about 16km off the southern island of Lampedusa.
Coastguard officials said 70 people had been rescued and 10 bodies, including four women, had been recovered.
Survivors reported there had been up to 120 immigrants on board.
Such estimates could be inexact so it was difficult to estimate how many were missing, officials said.
Lampedusa, between Sicily and Libya, has become a gateway for illegal immigrants and refugees who leave north Africa in an attempt to enter the European Union.
One navy ship had been following the immigrant boat and was able to start the rescue quickly, hence the high number of survivors, the coastguard said.
Survivors said the boat turned over when the immigrants saw the navy vessel and many of them moved abruptly to one side.
Amato, the Italian interior minister, called for more co-operation to "dismantle once and for all the criminal organisations that daily put the lives of so many as risk in a Mediterranean crossing".
The growing number of illegal migrants seeking to escape poverty has become one of Europe's biggest political issues.
"What happened today is not only a tragedy but nothing less than a crime"
Italy's Interior Minister
Immigrants pay unscrupulous gangs in Africa thousands of dollars for their journey. Many of them are repatriated back to Africa if they are caught unless they can prove that they are political refugees.
Nearly 10,000 have reached Lampedusa so far this year. In 2005 nearly 23,000 illegal immigrants reached Italy, some 8,000 more than in 2004.
European Union countries which are the strongest magnets for illegal immigration, including Spain, Italy, Greece and Malta, have asked the bloc for help.
The European Commission has proposed that the EU's 25 member states create a permanent rapid reaction force to deal with sudden major influxes of illegal migrants.
European and African governments agreed to crack down on human trafficking at a meeting in Rabat last month.