German Vice Chancellor Sigmar Gabriel says the nationalist Alternative for Germany party should be observed by the agency that tracks extremists after comments from its leader suggesting police should be allowed to shoot refugees trying to enter the country.

Gabriel told Bild newspaper Sunday he has "massive doubt" the party supports Germany's "free democratic order."

His comments come after party head Frauke Petry told the Mannheimer Morgen newspaper police "must stop illegal border crossings, and also make use of their firearm if necessary."

Joerg Radek, vice-chairman of police union GdP, called Petry's suggestion "radical and inhumane" and accused her of seeking to "exploit the police."

Radek says "this is something we have already once had in our history in Germany and we don't want it ever again."