“We must not send out false signals and must absolutely prevent any more people risking their lives in the dangerous passage across the Mediterranean,” Mr Kurz said.
Italy countered with its own proposals to deal with the problem by deterring migrants from attempting the crossing.
Enzo Moavero Milanesi, the Italian foreign minister, called on Sunday for specially chartered flights to bypass the Mediterranean altogether.
Under the Italian proposals, the EU would decide migrants’ asylum claims in north Africa and fly those granted refugee status to be flown to Europe.
“Those who have the right to asylum must be able to travel in dignified conditions, not in the hands of criminals,” Mr Milanesi told Corriere della Sera newspaper.
“Migrants are not looking for Italian, Greek or Maltese shores. They are looking for Europe. Therefore we must find a solution within a European framework.”
Operation Triton, the EU’s rescue mission, ended last year, leaving only ships manned by volunteer organisations to rescue migrants from drowning.
But Italy has refused to allow the volunteer ships to land at its ports even if other EU states agree to take the migrants on board.
Matteo Salvini, the hardline Italian interior minister, has rejected a formal request from Germany to open its ports