Denmark said it would disregard a European Union directive to lift temporary border restrictions within six months unless the bloc "miraculously" secured its external frontiers against undocumented migrants.

More than a million people sought asylum in the EU in 2015. An EU deal with Turkey last year reduced the influx to a trickle though thousands of migrants are still reaching Europe from Libya via sea routes to Italy.

With the number of arrivals well down since 2015, the European Commission said on May 2 that Germany, Austria, Denmark and Norway should remove lift border controls within six months.

But Danish Prime Minister Lars Løkke Rasmussen told parliament on Tuesday that the flow of refugees and migrants into Italy and further into Europe "is (still) far too high".

"We will continue border controls unless the EU miraculously finds ways to regain control of its outer frontiers and Italy curbs the flow of refugees onto (its territory) and further into Europe," he added.

As part of the EU's response to the surge of refugees and migrants in 2015, the bloc approved emergency controls in its passport-free Schengen travel zone, despite concerns about the impact on trade.

Earlier this month, the EU executive approved maximum six-month extensions of controls at the German-Austrian border, Austria's frontiers with Slovenia and Hungary and at Danish, Swedish and Norwegian borders. Norway is in the Schengen zone but outside the EU. The Swedish government has said it will remove ID checks on journeys from Denmark into Sweden. Germany has argued that despite the fall in migrants coming through Greece and the Western Balkans, it needs the controls to counter the threat of militancy in Europe.

Denmark, known for its long history of high human rights standards, tolerance and openness, has become the least attractive country in Europe for refugees and asylum seekers thanks to its anti-refugee policies. The country has not only reinstated border controls to stem the flow of refugees into the country, those who are already in the country have been slapped with a new refugee law that aims to make the country an unwanted destination for migrants, scaring them away by imposing harsh policies; stripping refugees of jewelry to pay for their aid and potentially sending them to state-backed refugee villages with extended waiting periods for family reunification of up to three years. Anti-immigration sentiment has been on the rise in the country as police arrested a Dane for trying to blow himself up at an asylum center last August.