Schulz will stand as the center-left Social Democratic Party (SPD) candidate for Chancellor in the poll scheduled for September.
A speech by Bjoern Hoecke, the AfD's leader in the eastern state of Thuringia, on Tuesday triggered anger across Germany and even caused one member of the radical Left party to report him for incitement to racial hatred.
Bavarian Christian Social Union has been a loud critic of Merkel's refugee policy from her own side.
The German Chancellor is under more pressure amidst populist right-wing resurgence.
Alternative For Germany is outflanking German Chancellor to the right.
"They want to go back to the repressed West German republic of the 1960s," Sigmar Gabriel said.
Country may be set to elect the EU's first hard-right head of state.
A rift in the German hard-right party is deepening.
Electorates across Europe must note history, writes the president of the European Jewish Congress.
The party's popularity surge comes a week ahead of crucial state legislature votes.
The poll also found a surge in support for anti-immigrant party AfD.