Vice Chancellor Sigmar Gabriel told Bild newspaper that "there is massive doubt that (the Alternative for Germany party) stand by the free democratic order of the republic."
Frauke Petry, the head of the party also known by its German initials AfD, told the Mannheimer Morgen daily yesterday that a border police officer "must stop illegal border crossings, and also make use of his firearm if necessary."
Germany saw nearly 1.1 million asylum-seekers enter the country last year and the AfD has been gaining in support as more people question whether the government will be able to deal with the influx.
Joerg Radek, vice-chairman of the GdP police union, slammed Petry's suggestion, saying no German police officer would shoot at a refugee.
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"Whoever proposes such a radical approach apparently wants to overturn the rule of law and exploit the police," he said in a statement.
Baden-Wuerttemberg governor Winfried Kretschmann, a member of the Greens party that is in opposition at the federal level, told Berlin's Tagesspiegel newspaper the chancellor's insistence on "working step by step" on a European solution to the refugee crisis was the correct path.
"Which of her counterparts in the EU will hold Europe together if she fails?" he asked. "Far and wide there's nobody in sight. Therefore I pray every day that the chancellor remains healthy."
Europe has endured a huge influx of migrants, most of whom undertake a dangerous journey in search of a better life. Yesterday, at least 37 people drowned, including children and babies, when their boat capsized during the short trip from Turkey to Greece.