Rome plans to ask the European Union to amend the rules of the Sophia mission, currently commanded by Italy, and rotate the ports where immigrants rescued at sea can disembark, and France and Spain are expected to top the list.
Currently, all ships dock in Italy, but Rome's new right-wing nationalist government says it should not have to shoulder the burden alone and it's time for other EU states to do their fair share by hosting more immigrants.
In comments before the informal talks of EU defense ministers, Mogherini asked them to show a "constructive attitude" to work to continue the mission.
"So far no consensus has been reached … We definitely can not afford to abandon an EU operation without clarity about the rules it must follow," he said before the meeting in Vienna.
"It would be good if the member states take more responsibility," he added. "The important thing is that we managed to keep the operation going … This has been a remarkable achievement for the entire European Union."
German Defense Minister Ursula von der Leyen said that Sophia's mandate was until the end of the year, when she expected EU leaders to resolve the question of how asylum-seekers arriving in Europe whose claims are recognized should be distributed among the member states. .
"That is the question that, however, is at the top of the agenda of the EU leaders … so I hope that this issue will be resolved in the autumn," he said.
The leaders of the EU will meet in September in the Austrian city of Salzburg to analyze the crisis of immigrants. Austria currently holds the rotating presidency of the EU.
Sophia was launched in June 2015 after a series of deadly shipwrecks and has since collected thousands of migrants struggling in the Mediterranean.
According to the newspaper La Stampa, the idea of Italy is to rotate the landings between the ports of the Mediterranean, with a particular emphasis on France and Spain, and with Greece and Malta also sharing the cargo.
Italian Defense Minister Elisabetta Trenta said Wednesday night that the ball was in the EU field.
"By accepting our proposal, (the EU) will have the opportunity to demonstrate that it is a real community of values and intentions, and by rejecting it, it will deny its own fundamental principles," he said.
Italy has been rejecting ships with migrants rescued at sea in a campaign to get EU countries to take their part.
Last week, it threatened to stop billions of euros of EU funds on the issue, accusing Europe of backing down as Italy grapples with arrivals of seemingly endless migrants.