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Children of a welcome class for migrants attend a German language lesson at the catholic Sankt Franziskus school in Berlin, Germany, Jan. 22, 2016. REUTERS/HANNIBAL HANSCHKE

A group of European Union countries including Germany is pushing for an extension of border controls in the Schengen free-travel zone to help cope with Europe's migration crisis, the Welt am Sonntag newspaper reported.

In a pre-released story, the Sunday newspaper said Austria, Belgium, Sweden and Denmark were also among those pressing for the extension of the checks on selected Schengen borders.

The initiative will be discussed at a meeting of EU interior ministers in Amsterdam on Monday, the paper reported.

If successful, it would allow Germany to prolong its border controls, due to lapse in May, for a further 1-1/2 years.

More than one million people arrived in Europe last year, mostly fleeing war and poverty in the Middle East and north Africa, and the numbers show little sign of falling.

Six Schengen members, including Germany and four other EU countries, have reinstated temporary border checks in the passport-free area.

The 26-nation Schengen free travel area, a centerpiece of European integration, is under pressure from the hundreds of thousands of migrants and refugees trying to reach the most prosperous EU member states. Many first arrive in Greece.

Austrian Interior Minister Johanna Mikl-Leitner threatened Greece with suspension from the free-travel zone if it fails to do more to control immigration, a suggestion other EU governments, notably in Eastern Europe, have also made.

"If the government in Athens does not finally do more to secure the outer borders, then we will have to openly discuss a temporary expulsion of Greece from the Schengen area," she told Welt am Sonntag. "It is a myth that the Greek-Turkish border cannot be controlled."

Austria announced on Wednesday that it would cap the number of people allowed to claim asylum this year at 37,500, less than last year's total, and reduce the ceiling annually to 25,000 by 2019.

European leaders meeting in the Swiss resort of Davos warned the EU could unravel if member states fail to agree a common approach to the refugee crisis and security challenges in the next few months.