Wolfgang Sobotka believes closing off the crossing is “the only way to end the senseless and tragic dying in the Mediterranean”.
The calls come after almost 9,000 migrants were saved as they tried to reach Europe over the Easter weekend.
Mr Sobotka wants Europe to introduce measures to stop the migrant crisis from deepening
A rescue in the open sea cannot be a ticket to Europe, because it gives organised traffickers every argument to convince people to flee for economic reasons
Coastguards said they saved 8,360 refugees after they were cast off from Libya in a desperate bid to reach southern Italy.
Now, Mr Sobotka is calling on EU leaders to block the route in order to stop migrants taking grave risks to reach European shores.
Thousands of migrants were saved after trying to cross the Mediterranean over the Easter weekend
He said: “A rescue in the open sea cannot be a ticket to Europe, because it gives organised traffickers every argument to convince people to flee for economic reasons.”
Austria was instrumental in closing the Balkans route to asylum-seekers last year, and now Mr Sobotka suggests similar measures should be taken by countries on Europe’s southern border.
He added: “In the event of a sudden influx, we would be equipped and able to ramp up the border management within hours.
Migrant crisis: Key locations before and after
Tue, April 4, 2017
In these composite images, a comparison has been made between a scene at a key location during the height of the 2015 migrant crisis last year and the view there now
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Aid workers help migrants up the shore after making the crossing from Turkey to the Greek island of Lesbos on November 16, 2015 in Sikaminias, Greece
“There is no alternative to a European solution in which the EU’s external border is effectively protected.”
So far this year, more than 900 migrants are believed to have died while trying to cross the Mediterranean and there are fears that improving weather could result in increasing attempts to embark on the dangerous crossing.
The asylum-seekers rescued over Easter weekend had set off from Libya
The boats used are often dangerously overcrowded and not fit for the dangerous journey.
European leaders are desperate to avoid a repeat of 2015 when more than one million migrants and refugees crossed into the continent, sparking a crisis as countries struggled to cope with the huge numbers of new arrivals.