The European Commission has called for the EU to launch Mediterranean-wide search and rescue patrols to intercept migrant boats.
The move by Home Affairs Commissioner Cecilia Malmstroem was prompted by the deaths of at least 274 migrants whose boat sank off Italy's Lampedusa island.
She said this was a moment to show real European solidarity beyond words.
The alleged skipper of the Lampedusa boat, a Tunisian man, is being held in Sicily, suspected of manslaughter.
Ms Malmstroem told reporters after the meeting she had asked ministers from the 28 member states to allow a major operation by the EU's Frontex border agency "covering the whole Mediterranean, from Cyprus to Spain".
First reactions from EU member states were encouraging, she said.
"We will ask Frontex to make a concrete proposal and come back to us," she said.
Frontex is currently helping Italy to intercept migrant boats, but the two EU operations in the southern Mediterranean have limited resources - a total of four ships, two helicopters and two planes.
The search and rescue patrols would "help better tracking, identification and rescue of boats, especially migrants' boats", the commissioner's spokesman Michele Cercone said.
"It could help prevent tragedies like the one in Lampedusa," he added.
The search for bodies from the boat that sank on Thursday off Lampedusa, between Sicily and Africa, continued throughout Tuesday.
Divers, who have already recovered dozens of bodies, brought up another 42, bringing the total number to 274. One of those brought to the surface was a child.
Many of the 500 people who were on board are still missing. The victims were mostly from Eritrea and Somalia.
The alleged captain of the ship, Khaled Bensalam, 35, is in custody in Agrigento, Sicily. Investigators suspect him of being responsible for the sinking and he could face multiple counts of manslaughter, though no charges have yet been laid, the BBC's Rome office was told.
Until his arrest, he was with other survivors of the shipwreck at the reception centre in Lampedusa, Italian media report.
It is thought that other than the skipper, there was only one crewman aboard, and that he did not survive.
In Luxembourg, Ms Malmstroem asked EU member states to "give their political support and to make the necessary resources available".
The EU's external border agency, set up in 2004, has seen its budget cut from 118m euros (£100m; $160m) in 2011 to 85m euros in 2013.
Tens of thousands of migrants attempt the perilous crossing from North Africa to Sicily and other Italian islands each year.
Accidents are common, but last week's shipwreck was among the deadliest on record.
Co-operation had to be increased, the EU commissioner said, with migrants' countries of origin and the countries from which they travelled to Europe.
A partnership with Morocco was already in place and the EU would hope to do the same with Tunisia and other North African states.
Italian Interior Minister Angelino Alfano backed the European Commission plan, arguing that more had to be done to save lives. "We are in the middle of the Mediterranean: we have saved thousands and thousands of people - now we are asking the EU for a hand in strengthening border control," he said.
However, there was some concern among diplomats that the new mission was doomed to failure. One told AFP that it would result in migrant boats taking to sea as soon as they saw the Frontex ships in order to be rescued.
There were 155 survivors of the Lampedusa accident, which happened about 1km (half a mile) offshore.
The wreck is lying about 47m (155ft) below the surface, which means the recovery divers can only stay on the bottom for a short time.
Divers have begun removing bodies from the hull, where a navy officer said they found corpses "so entwined one with the other" they were difficult to pull out.
Malta and Greece, as well as Italy, have long made appeals previously for more assistance from the EU for the states that bear the brunt of mass immigration.
The UN refugee agency is also urging EU countries to share the immigration burden more equally.
A spokesman told the BBC that the experience of a small Italian island handling large numbers of migrants clearly showed how southern Europe was having to deal with an unfair share of the problem.
But northern EU nations, such as Sweden, Germany and Denmark, insist they take a large proportion of migrants. "Germany is the country that takes in the most refugees in Europe," Interior Minister Hans-Peter Friedrich said on Tuesday.
A spokesman in Berlin told German media that 65,000 refugees had been taken in last year, compared with 15,000 in Italy.
EU states have for years been unable to reach agreement on a common migration and asylum policy.
Italian PM Enrico Letta is expected to travel to Lampedusa on Wednesday with Ms Malmstroem and European Commission President Jose Manuel Barroso.
Key migrant routes to southern Europe