"The EU has found itself under the onslaught of hundreds of thousands of migrants and has ceased to be a safe place," Fico told parliament, insisting that "90 percent of these people are economic migrants."
"There may be several thousand potentially very dangerous persons" among those who have arrived, he added, pointing to concerns over Islamic State jihadists slipping into the EU under the guise of refugees.
"Our safety is of paramount importance."
The Slovak leader has been among the most vocal opponents of a European Commission proposal for fixed quotas designed to distribute migrants across the EU.
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A social democrat, Fico also warned that the unprecedented influx of refugees and migrants from war-torn parts of the Middle East and North Africa into the EU could fuel the rise of the far right.
"If we do not stop the wave of migrants, there is a danger that the traditional pro-European parties will be replaced by nationalistic, xenophobic and anti-European parties," he said.
Unlike EU neighbours Austria and Hungary, Slovakia has seen few refugees and migrants seeking to transit through its territories to Germany in recent months.
The eurozone member of 5.4 million people joined the European Union in 2004.