Merkel, who has previously expressed doubts about Turkey ever joining the European Union, refused to commit to the same move, but sharply criticized Erdogan's rule, saying that "Turkey is departing from all democratic practices at breakneck speed".
"If I become German chancellor, if the people of this country give me a mandate, then I will propose to the European Council that we end the membership talks with Turkey", Schulz said.
She said she will discuss with European Union counterparts to see if "we can end these membership talks", adding that "I don't see (Turkey) ever joining and I had never believed that it would happen".
Social Democrat Martin Schulz, Merkel's main challenger, said she made a "serious mistake" when she opened Germany's boarders to around a million asylum seekers. That prompted a testy response by the chancellor, who's seeking a fourth term in the federal election on September 24.
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"I don't think that one can solve this conflict without the American President", she said.
Schulz, who had previously complained that Merkel was lulling voters to sleep with her refusal to engage in combative debate, went on the offensive quickly.
In addition, 77 per cent of the survey respondents said that Merkel did well, as expected, while 55 per cent said Schulz's performance was better than expected.
Merkel has been chancellor since 2005 and is widely seen as Europe's most influential politician.
Schulz's campaign got off to a promising start early this year, with thousands flocking to the party after he was chosen as candidate; but three crushing defeats at the hands of the conservatives in regional elections, including in its heartland of North Rhine-Westphalia, knocked him off course. "There are moments in the life of a leader or a chancellor where you just have to take decisions".