“The Schengen zone may not last long without controlling its borders if the system of protection of its external borders is not functioning,” the Minister said on Saturday.

Thomas de Maiziere added that the possible closure of the Schengen borders was discussed as part of a public debate in September when a proposal to close the German borders to the incoming migrants was rejected.

“However, just how long this may continue if the number of incoming migrants remains this high is another matter,” the Interior Minister added.

Angela Merkel, the German chancellor, has resisted calls to set limits on those fleeing countries such as Syria.

The influx of refugees entering Germany this year has passed the one million mark, ramping up pressure on European leaders as they struggle to cope with the migrant crisis.

The number of arrivals for the year so far was more than four times the total for all of 2014 with Germany now the top European destination for people fleeing conflict, repression and misery in the Middle East, Asia and Africa.