At a meeting in Paris President Emmanuel Macron and Italy's new premier Giuseppe Conte also called for "profound" changes to the EU's asylum rules, which put the migrant burden on their port of entry to Europe -- mainly Italy and Greece.
The two leaders were at pains to put on a united front after a bitter row this week between Macron and the new populist government in Rome over Italy's rejection of a rescue boat with hundreds of migrants on board.
The clash underscores deep splits in Europe over how to handle the massive influx of migrants from across the Mediterranean in recent years.
In Germany, Chancellor Angela Merkel is embroiled in a showdown with the right wing of her governing coalition, which is demanding that she immediately ditch her liberal migration policy and tighten border controls.
Conte called for "European protection centres" to process asylum claims in migrants' countries of origin -- currently mainly Africa -- "before their arrival in Europe".
"We must prevent these voyages of death," he said of the perilous crossings in flimsy boats.
His comments were echoed by Macron, who said EU members should send immigration officials "to the other side" of the Mediterranean.
The French leader, who sparked fury in Rome this week by accusing Italy of "cynicism and irresponsibility" for leaving 629 migrants drifting at sea, also called for tighter controls of the EU's external borders.
"We cannot take in everybody," he said, repeating his view that those not fleeing war should be sent home.
He said France and Italy should team up with Spain and Germany to come up with "new initiatives" to resolve the crisis.
There have been few signs that European leaders are ready to coordinate their policies despite a looming end-of-June deadline to change the EU's current asylum rules.
In Berlin, Merkel was fighting Friday to save her government, with her interior minister Horst Seehofer openly defying her moderate line on migration.
An opinion poll by Infratest Dimap suggests 62 percent of Germans back the tougher stance favoured by Seehofer, including turning back undocumented migrants at the border and deporting failed asylum seekers faster.