Already represented in five of Germany's 16 regional parliaments, the AfD has campaigned on slogans such as "Secure the borders" and "Stop the asylum chaos".
German Vice-Chancellor Sigmar Gabriel said on Saturday that gains for the AfD would not change his government's stance on immigration.
He said: "There is a clear position that we stand by: humanity and solidarity. We will not change our position now.
But in Berlin on Saturday, about 2,000 right-wing demonstrators carrying German flags chanted "Merkel must go!" and "We are the people!".